Class 10 The Quadratic Formula — practice questions with answers

Algebra — Quadratics · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The quadratic formula for ax² + bx + c = 0 (a != 0) gives x = ?

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Answer: A) x =

\frac{- b \pm b ^{2} - 4 a c}{2 a}

The standard quadratic formula is x =

\frac{- b \pm b ^{2} - 4 a c}{2 a}

2. Solve x² - x - 1 = 0. The positive root (golden ratio) equals:

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Answer: A)

\frac{1 + 5}{2}

D = 1 + 4 = 5. x =

\frac{1 \pm 5}{2}

. Positive root =

\frac{1 + 5}{2}

3. If b² - 4ac for ax² + bx + c = 0 (a, b, c rational) is positive
but NOT a perfect square, the roots are:

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Answer: A) real, distinct and irrational

D > 0 gives distinct real roots; since D is not a perfect square,

D

is irrational, so the roots are irrational.

4. Solve 9x² - 12x + 4 = 0 by the quadratic formula. The solution is:

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Answer: C)

\frac{2}{3}

, twice

D = 144 - 144 = 0, so

D = 0

and the

\pm

collapses. x =

\frac{12}{18} = \frac{2}{3}

, a repeated root. (Dividing 12 by a = 9 instead of 2a = 18 gives the wrong value

\frac{4}{3}

5. Which statement about the quadratic formula is NOT true?

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Answer: C) If D is negative the formula still gives two real roots

A negative discriminant makes

D

non-real, so there are no real roots — that statement is false. The others are true: D = 0 gives the repeated root

- \frac{b}{2 a}

; adding

\frac{- b + D}{2 a}

and

\frac{- b - D}{2 a}

gives

\frac{- 2 b}{2 a} = - \frac{b}{a}

; and the derivation only needs a

\neq =

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