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Quadratic Basics: 18 MCQs with answers

All 18 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 17 Quick Revision · 15

Warm-up · 7 questions

Q1. Which of the following is the standard form of a quadratic equation?

Beginner
A $a/x^2 + b/x + c = 0$ B $ax + b = 0$ C $ax^3 + bx^2 + cx + d = 0$ D $ax^2 + bx + c = 0$
Show answer & explanation

$ax^2 + bx + c = 0$

The standard form of a quadratic equation is $ax^2 + bx + c = 0$, where $a \neq 0$.

Q2. In the equation $2x^2 - 3x + 5 = 0$, what is the value of $a$?

Beginner
A 5 B -3 C 2 D 0
Show answer & explanation

2

In the standard form $ax^2 + bx + c = 0$, $a$ is the coefficient of $x^2$, which is 2.

Q3. Which of the following is a quadratic equation?

Beginner
A $x^2 + 2x + 1 = 0$ B $x + 3 = 0$ C $x^3 - 1 = 0$ D $2x - 5 = 0$
Show answer & explanation

$x^2 + 2x + 1 = 0$

A quadratic equation has degree 2, so $x^2 + 2x + 1 = 0$ is quadratic.

Q4. The roots of the equation $x^2 - 9 = 0$ are:

Beginner
A 3 and 3 B 9 and -9 C 3 and -3 D 0 and 9
Show answer & explanation

3 and -3

$x^2 - 9 = (x-3)(x+3) = 0$, so $x = 3$ or $x = -3$.

Q5. Which of the following is NOT a quadratic equation?

Beginner
A $2x^2 - 3x = 0$ B $x^2 + 1 = 0$ C $x^2 + 2x + 1 = 0$ D $x^3 + x^2 + 1 = 0$
Show answer & explanation

$x^3 + x^2 + 1 = 0$

A quadratic equation has degree 2; $x^3 + x^2 + 1 = 0$ is cubic.

Q6. The equation $x^2 + 2x + 1 = 0$ has two distinct real roots.

Beginner
A True B False
Show answer & explanation

False

The discriminant is $4 - 4 = 0$, so it has equal real roots, not distinct.

Q7. The roots of the equation $x^2 - 5x + 6 = 0$ are 2 and 3.

Beginner
A True B False
Show answer & explanation

True

Factorizing gives $(x-2)(x-3)=0$, so roots are indeed 2 and 3.

Building up · 11 questions

Q8. What are the roots of the equation $x^2 - 5x + 6 = 0$?

Intermediate
A -1 and -6 B 1 and 6 C -2 and -3 D 2 and 3
Show answer & explanation

2 and 3

Factorizing: $x^2 - 5x + 6 = (x-2)(x-3) = 0$, so $x=2$ or $x=3$.

Q9. Which of the following is a root of $2x^2 - 4x = 0$?

Intermediate
A 2 B 4 C 0 D -2
Show answer & explanation

0

Factorizing: $2x(x-2) = 0$, so $x=0$ or $x=2$. Thus 0 is a root.

Q10. The equation $x^2 + 4x + 4 = 0$ has roots:

Intermediate
A 2 and 2 B -2 and -2 C 4 and 0 D -4 and 0
Show answer & explanation

-2 and -2

$x^2 + 4x + 4 = (x+2)^2 = 0$, so $x = -2$ (double root).

Q11. What is the product of the roots of $x^2 - 7x + 12 = 0$?

Intermediate
A -7 B 7 C -12 D 12
Show answer & explanation

12

For $ax^2 + bx + c = 0$, product of roots = $c/a = 12/1 = 12$.

Q12. The sum of the roots of $3x^2 - 6x + 2 = 0$ is:

Intermediate
A 2 B -2 C 6 D -6
Show answer & explanation

2

Sum of roots = $-b/a = -(-6)/3 = 2$.

Q13. Which of the following equations has roots 5 and -2?

Intermediate
A $x^2 - 3x + 10 = 0$ B $x^2 + 3x - 10 = 0$ C $x^2 + 3x + 10 = 0$ D $x^2 - 3x - 10 = 0$
Show answer & explanation

$x^2 - 3x - 10 = 0$

Sum = 3, product = -10, so equation is $x^2 - 3x - 10 = 0$.

Q14. The factorization of $x^2 - 4x - 5$ is:

Intermediate
A $(x+5)(x-1)$ B $(x-5)(x-1)$ C $(x-5)(x+1)$ D $(x+5)(x+1)$
Show answer & explanation

$(x-5)(x+1)$

We need two numbers whose product is -5 and sum is -4: -5 and 1, so $(x-5)(x+1)$.

Q15. What is the discriminant of $x^2 + 2x + 1 = 0$?

Intermediate
A 4 B 0 C 8 D -4
Show answer & explanation

0

Discriminant $D = b^2 - 4ac = 4 - 4(1)(1) = 0$.

Q16. The equation $x^2 - 4x + 4 = 0$ has:

Intermediate
A Two equal real roots B No real roots C Two distinct real roots D One real and one imaginary root
Show answer & explanation

Two equal real roots

Discriminant $D = 16 - 16 = 0$, so roots are real and equal.

Q17. The roots of $x^2 + 6x + 9 = 0$ are:

Intermediate
A 6 and 0 B 3 and 3 C -6 and 0 D -3 and -3
Show answer & explanation

-3 and -3

$x^2 + 6x + 9 = (x+3)^2 = 0$, so $x = -3$ (double root).

Q18. The value of $k$ for which $x = 2$ is a root of $x^2 - 3x + k = 0$ is:

Intermediate
A 2 B 6 C -2 D -6
Show answer & explanation

2

Substitute $x=2$: $4 - 6 + k = 0 \Rightarrow k = 2$.

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