Quadratic Equation

Online MCQs Intermediate Mathematics from Chapter 4 Quadratic Equation with Questions and Answers

MCQs Quadratic Equations Questions 3

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The post is about Multiple Choice Questions from Chapter 4 of Intermediate First-Year Mathematics. The Quiz is about Quadratic Equations Questions with Answers. There are 28 MCQ Type Questions with answers. Let us start with the quiz “Quadratic Equations Questions”.

Online Multiple Choice Questions about Quadratic Equations First Year Mathematics with Answers

1. If $S$ and $P$ are the sum and product of the roots of a quadratic equation then the equation is

 
 
 
 

2. The fourth roots of unity are

 
 
 
 

3. A quadratic equation is also called

 
 
 
 

4. If $p$ and $q$ are the roots of $8x^2-3x-16=0$ then $pq$ is equal to

 
 
 
 

5. $x^2-x-6=0$ has roots

 
 
 
 

6. If the discriminant is positive and not a perfect square then the roots are

 
 
 
 

7. If the roots $px^2+qx+1=0$ are equal then

 
 
 
 

8. If $\alpha$ and $\beta$ are the roots of $3x^2-2x+4=0$ then the value of $\alpha+\beta$ is

 
 
 
 

9. For any $n\in Z, $\omega^n$ is equivalent to one of

 
 
 
 

10. The synthetic division is a process of

 
 
 
 

11. If the discriminant is negative, then the roots are

 
 
 
 

12. The basic techniques for solving quadratic equations is/ are

 
 
 
 

13. The equation of the form $(x+a)(x+b)(x+c)(x+d)=k$, where $a+b=c+d$, can be converted into

 
 
 
 

14. A quadratic equation $Ax^2+Bx+C=0$ becomes a linear equation if

 
 
 
 

15. $\omega^{28}+\omega^{29}+1=$?

 
 
 
 

16. The degree of a quadratic equation is

 
 
 
 

17. The roots of $ax^2+bx+c=0$ are imaginary, if

 
 
 
 

18. To solve $ax^2  + bx+c=0$ where $a, b,c \in R and $a\ne 0$, we can use

 
 
 
 

19. The roots of $2x^2-bx + 8=0$ are imaginary, if

 
 
 
 

20. If the roots of $ax^2+bx+c=0$, ($a\ne 0$) are real then

 
 
 
 

21. The roots of $ax^2+bx+c=0$ are equal, if

 
 
 
 

22. If the discriminant is a positive and perfect square then the roots are

 
 
 
 

23. If 2 and -5 are roots of a quadratic equation then the equation is

 
 
 
 

24. The equation of the form $ax^2+bx+c=0$ where $a, b, c \in R$, and $a\ne 0$ is called

 
 
 
 

25. The graph of a quadratic equation is

 
 
 
 

26. If $ax^2+bx+c=0$ then the discriminant is

 
 
 
 

27. If the discriminant is zero, then the roots are

 
 
 
 

28. The roots of equation $x^2+2x+3=0$ are

 
 
 
 

The standard form of a quadratic equation is written as:

$$ax^2+bx+c=0$$

where:

$a, b$, and $c$ are coefficients (numbers), and $x$ is variable, provided that $a \ne 0$ (otherwise it would not be a quadratic equation).

Online MCQs Quadratic Equations Questions

Quadratic Equations Questions Intermediate Mathematics First Year
  • If 2 and -5 are roots of a quadratic equation then the equation is
  • If $S$ and $P$ are the sum and product of the roots of a quadratic equation then the equation is
  • If $\alpha$ and $\beta$ are the roots of $3x^2-2x+4=0$ then the value of $\alpha+\beta$ is
  • If $p$ and $q$ are the roots of $8x^2-3x-16=0$ then $pq$ is equal to
  • If $ax^2+bx+c=0$ then the discriminant is
  • If the roots of $ax^2+bx+c=0$, ($a\ne 0$) are real then
  • The roots of $ax^2+bx+c=0$ are imaginary, if
  • The roots of $ax^2+bx+c=0$ are equal, if
  • If the discriminant is a positive and perfect square then the roots are
  • If the discriminant is positive and not a perfect square then the roots are
  • If the discriminant is negative, then the roots are
  • If the discriminant is zero, then the roots are
  • The roots of $2x^2-bx + 8=0$ are imaginary, if
  • The equation of the form $ax^2+bx+c=0$ where $a, b, c \in R$, and $a\ne 0$ is called
  • A quadratic equation is also called
  • The degree of a quadratic equation is
  • The graph of a quadratic equation is
  • The basic techniques for solving quadratic equations is/ are
  • To solve $ax^2  + bx+c=0$ where $a, b,c \in R and $a\ne 0$, we can use
  • The equation of the form $(x+a)(x+b)(x+c)(x+d)=k$, where $a+b=c+d$, can be converted into
  • For any $n\in Z, $\omega^n$ is equivalent to one of
  • $\omega^{28}+\omega^{29}+1=$?
  • The fourth roots of unity are
  • The synthetic division is a process of
  • $x^2-x-6=0$ has roots
  • The roots of equation $x^2+2x+3=0$ are
  • If the roots $px^2+qx+1=0$ are equal then
  • A quadratic equation $Ax^2+Bx+C=0$ becomes a linear equation if

Applications of Quadratic Equations

Quadratic equations have various applications in many fields, including:

  • Projectile motion
  • Circuit analysis
  • Optimization problems

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MCQs Quadratic Equations First Year 2

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The post concerns MCQs Quadratic Equations Chapter 4 of Intermediate Mathematics the first year. There are 20 questions and each question and its options appear randomly. The quiz will help First-year (Intermediate) Pre-Engineering mathematics students prepare for the examination. Let us start with MCQs Quadratic Equations First Year Mathematics with Answers.

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MCQs Quadratic Equations with Answers

  • The complex cube roots of unity are ———– each other.
  • The complex fourth roots of unity are ——— each other.
  • If the sum of all cube roots unity is equal to $x^2+1$ then $x$ is equal to
  • If the product of all cube roots of unity is equal to $\rho^2+1$ then $p$ is
  • The complex fourth roots of unity are ———- each other.
  • The expression $a_nx^n + a_{n-1}x^{n-1}+\cdots + a_1x+a_0$. $a\ne 0$ is a polynomial of degree $n$ if $n$ is any$
  • The expression $x^2+\frac{1}{x} -3$ is
  • If $f(x)$ is divided by $x-a$ then Divided = (divisor)(—–)+Remainder.
  • If $f(x)$ is divided by $x-a$ then by remainder theorem, the remainder is
  • The polynomial ($x-a$) is a factor of $f(x)$ if and only if
  • $x-2$ is a factor of $x^2-kx +4$ if $k$ is
  • If $x=-2$ is a root of $kx^4-13x^2+36=0$ then $k=$
  • $x+a$ is a factor of $x^n+a^n$ when $n$ is
  • $x-a$ is a factor of $x^n-a^n$ if $n$ is
  • Sum of roots of $ax^2-bx-c=0$ is ($a\n-0$)
  • Product of $ax^2-bx -c=0$ is ($a\ne 0$)
  • The sum of the roots of any quadratic equation is
  • The product of roots of any quadratic equation is
  • If sum of roots of $7x^2+px+q=0$ is q then $q=$
  • If product of roots of $7x^2-px+q=0$ is 1 then $q=$
Chapter 4 MCQs Quadratic Equations

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Quadratic Equations Quizzes

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The following is the list of online MCQs Quadratic Equations Quizzes with Answers from the First-Year Mathematics Book of Intermediate Part-I. Click the links below to start with the Online MCQs Quadratic Equations Quizzes.

Quadratic Equations Quizzes

MCQs Quadratic Equations 1MCQs Quadratic Equations 1MCQs Quadratic Equations 1
MCQs Quadratic Equations 3MCQs Quadratic Equations 2MCQs Quadratic Equations 1

Introduction to Quadratic Equations (Second Degree Equations)

A quadratic equation is a type of second-degree polynomial equation in a single variable. Quadratic equations are a fundamental part of algebra, and mastering “Quadratic Equations” is essential for solving a wide range of mathematical problems. These quizzes are designed to test your understanding, from basic concepts like factoring and the quadratic formula to more advanced applications. Whether you are a beginner or looking to refine your skills, these quizzes offer a fun and engaging way to challenge yourself, learn, and improve. Perfect for students, educators, or anyone eager to sharpen their math skills!

Formula of Quadratic Equation

An equation of the form $ax^2 + bx + c = 0$ is called a Quadratic Equation, where $a, b,$ and $c$ are all real numbers and $a\ne0$. The Formula of Quadratic Equations is a second-degree equation in variable $x$.

Quadratic Equations Quizzes

The following are some basic methods to solve a quadratic equation:

  • By Factorization
  • By Completing Square
  • By Quadratic Formula

Role of Quadratic Equations

The role of quadratic equations is important in

  • Understanding relationships: Quadratic Equations can model relationships between variables where one quantity affects another in a squared manner, which is useful in various scientific fields.
  • Optimization problems: Maximizing profits, minimizing materials, or finding the peak of a curve – quadratic equations can help find optimal solutions in these scenarios.

Summary

In essence, quadratic equations provide a fundamental framework for dealing with squared terms and their relationship with linear terms. This foundation proves valuable across various disciplines, making quadratic equations a cornerstone of mathematical modeling and problem-solving.

MCQs Quadratic Equations Quiz with Answers

MCQs Hypothesis Testing

MCQs Quadratic Equation 1

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First-year pre-engineering mathematics multiple choice questions online examination. The quiz is about the MCQS Quadratic Equation online examination. The quiz will help First-year (Intermediate) Pre-Engineering mathematics students prepare for the examination. There are 20 questions with answers. Let us start with the Online MCQs Quadratic Equation Quiz.

Please go to MCQs Quadratic Equation 1 to view the test

An equation of the form $ax^2 + bx + c = 0$ is called a Quadratic Equation, where $a, b,$ and $c$ are all real numbers and $a\ne0$. This generic form of Quadratic Equations is a second-degree equation in variable $x$.

MCQs Quadratic Equations

MCQs Quadratic Equations with Answers

  • The equation $ax^2 + bx + 9 =0$ will be quadratic if
  • Solution set of the equation $x^2 – 4x + 4 = 0$ is
  • The quadratic formula for solving the equation $ax^2 + bx + c =0$ is $(a\ne 0)$
  • The convert $ax^{2n} + bx^n + c =0 (a\ne 0) $ into quadratic form, the correction substitution
  • The equation in which variable quantity occurs in the exponent is called
  • To convert $ 4^{1+x} + 4^{1-x} =10$ into quadratic, the substitution is
  • The equation which remains unchanged if $x$ is replaced by $\frac{1}{x}$, then it is called
  • The equations involving radical expressions of the variable are called
  • The roots that satisfy the radical free equation but not the radical equation are called
  • The cube roots of unity are
  • The cube roots of $-1$ are
  • The sum of all cube roots of 64 is
  • The product of all cube roots of $-1$ is
  • $16\omega^4 + 16 \omega^8$
  • $(-1 + \sqrt{-3})^5 + (-1 – \sqrt{-3})^5$ is equal to
  • The sum of all four fourth roots of unity is
  • The product of all four fourth roots of unity is
  • The sum of all four fourth roots is 16 is
  • The product of all four fourth roots of 81 is
  • The complex cube roots of the unit are _______ each other

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