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Quadratic Equations: 15 MCQs with answers

All 15 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything

Warm-up · 8 questions

Q1. Which of the following is a quadratic equation?

Beginner
A $x^2 + 3x + 2 = 0$
B $\frac{1}{x} + x = 3$
C $2x + 5 = 0$
D $x^3 - 4x = 0$
Show the answer

A · $x^2 + 3x + 2 = 0$

A quadratic equation is of the form $ax^2 + bx + c = 0$ with $a \neq 0$. Only $x^2 + 3x + 2 = 0$ fits this form.

Q2. What is the standard form of a quadratic equation?

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

A · $ax^2 + bx + c = 0$

The standard form is $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and $a \neq 0$.

Q3. What is the discriminant of the quadratic equation $ax^2 + bx + c = 0$?

Beginner
A $4ac - b^2$
B $b^2 - 4ac$
C $a^2 - 4bc$
D $b^2 + 4ac$
Show the answer

B · $b^2 - 4ac$

The discriminant is $D = b^2 - 4ac$, which determines the nature of roots.

Q4. The quadratic formula to solve $ax^2 + bx + c = 0$ is:

Beginner
A $x = \frac{-b \pm \sqrt{b^2 + 4ac}}{2a}$
B $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
C $x = \frac{-b \pm \sqrt{4ac - b^2}}{2a}$
D $x = \frac{b \pm \sqrt{b^2 - 4ac}}{2a}$
Show the answer

B · $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q5. Find the roots of $x^2 - 4 = 0$.

Beginner
A $x = 2$ only
B $x = 2$ or $x = -2$
C $x = 4$ or $x = -4$
D $x = 0$ or $x = 4$
Show the answer

B · $x = 2$ or $x = -2$

$x^2 - 4 = 0$ gives $x^2 = 4$, so $x = \pm 2$.

Q6. Solve: $2x^2 - 8 = 0$.

Beginner
A $x = 2$ only
B $x = 0$ or $x = 4$
C $x = 2$ or $x = -2$
D $x = 4$ or $x = -4$
Show the answer

C · $x = 2$ or $x = -2$

$2x^2 - 8 = 0$ gives $x^2 = 4$, so $x = \pm 2$.

Q7. The equation $x^2 + 2x + 1 = 0$ has two distinct real roots.

Beginner
A True
B False
Show the answer

B · False

The discriminant is $2^2 - 4 \cdot 1 \cdot 1 = 0$, so the roots are equal, not distinct.

Q8. The quadratic formula can be used to solve any quadratic equation.

Beginner
A True
B False
Show the answer

A · True

The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ works for all quadratic equations.

Building up · 7 questions

Q9. Solve: $x^2 - 5x + 6 = 0$.

Intermediate
A $x = -1$ or $x = -6$
B $x = 1$ or $x = 6$
C $x = 2$ or $x = 3$
D $x = -2$ or $x = -3$
Show the answer

C · $x = 2$ or $x = 3$

Factorizing: $(x-2)(x-3)=0$, so $x=2$ or $x=3$.

Q10. If the discriminant of a quadratic equation is zero, then the roots are:

Intermediate
A Real and distinct
B Not real
C Zero
D Real and equal
Show the answer

D · Real and equal

When $D = 0$, the quadratic equation has two equal real roots.

Q11. What is the sum of the roots of the quadratic equation $ax^2 + bx + c = 0$?

Intermediate
A $\frac{b}{a}$
B $\frac{c}{a}$
C $-\frac{c}{a}$
D $-\frac{b}{a}$
Show the answer

D · $-\frac{b}{a}$

The sum of roots is $-\frac{b}{a}$.

Q12. What is the product of the roots of the quadratic equation $ax^2 + bx + c = 0$?

Intermediate
A $\frac{c}{a}$
B $-\frac{b}{a}$
C $\frac{b}{a}$
D $-\frac{c}{a}$
Show the answer

A · $\frac{c}{a}$

The product of roots is $\frac{c}{a}$.

Q13. If the discriminant of a quadratic equation is negative, then the roots are:

Intermediate
A Real and distinct
B Real and equal
C Zero
D Not real
Show the answer

D · Not real

When $D < 0$, the quadratic equation has no real roots.

Q14. Which of the following is a root of the equation $x^2 - 7x + 10 = 0$?

Intermediate
A 3
B 4
C 2
D 5
Show the answer

C · 2

Factorizing: $(x-2)(x-5)=0$, so roots are 2 and 5. Hence 2 is a root.

Q15. The roots of the quadratic equation $x^2 + 6x + 9 = 0$ are:

Intermediate
A Not real
B Zero
C Real and equal
D Real and distinct
Show the answer

C · Real and equal

Discriminant $D = 6^2 - 4 \cdot 1 \cdot 9 = 36 - 36 = 0$, so roots are real and equal.

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