Class 10 Roots by Factorisation — 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. Factorise and find the roots of x² - 5x + 6 = 0.

Ax = 2, 3
Bx = -2, -3
Cx = 1, 6
Dx = -1, -6

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Answer: A) x = 2, 3

x² - 5x + 6 = (x - 2)(x - 3) = 0, so x = 2 or x = 3.

2. Solve 6x² - x - 2 = 0.

Ax = $\frac{2}{3}$ , $- \frac{1}{2}$
Bx = $- \frac{2}{3}$ , $\frac{1}{2}$
Cx = $\frac{3}{2}$ , 2
Dx = $- \frac{3}{2}$ , -2

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Answer: A) x =

\frac{2}{3}

- \frac{1}{2}

6x² - x - 2 = (3x - 2)(2x + 1) = 0, so x =

\frac{2}{3}

or x =

- \frac{1}{2}

3. Solve 9x² - 16 = 0. The roots are:

Ax = $\frac{4}{3}$ , $- \frac{4}{3}$
Bx = $\frac{3}{4}$ , $- \frac{3}{4}$
Cx = $\frac{16}{9}$ , $- \frac{16}{9}$
Dx = 4, -4

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Answer: A) x =

\frac{4}{3}

- \frac{4}{3}

9x² - 16 = (3x - 4)(3x + 4) = 0, so x =

\frac{4}{3}

or x =

- \frac{4}{3}

4. Meena bought some sarees for Rs 600. If each saree had cost Rs 10 less, she could have bought 1 more saree for the same money.
Which quadratic in the price x (per saree, in Rs) models this?

Ax² - 10x - 6000 = 0
Bx² + 10x - 6000 = 0
Cx² - 10x + 6000 = 0
Dx² + 10x + 6000 = 0

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Answer: A) x² - 10x - 6000 = 0

\frac{600}{x - 10} - \frac{600}{x} = 1

. So 600x - 600(x-10) = x(x-10), 6000 = x² - 10x, giving x² - 10x - 6000 = 0.

5. A field is in the shape of a rectangle whose diagonal is 17 m. The length exceeds the breadth by 7 m.
Let breadth = x. Using the diagonal (Pythagoras) and factorisation, find the length (in m).

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Answer: A) 15

x² + (x+7)² = 17² = 289, so 2x² + 14x + 49 = 289, i.e. 2x² + 14x - 240 = 0, x² + 7x - 120 = 0 = (x + 15)(x - 8). Breadth x = 8, so length = 8 + 7 = 15 m.

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