Solve the following quadratic equations by factorization method: [2 MARKS]

(i) $x^{2} - 8 x + 16 = 0$

(ii) $x^{2} + 14 x - 32 = 0$

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Solution

Each factorisation : 1 Mark

(i) We have

$x^{2} - 8 x + 16 = 0$

$\Rightarrow (x - 4)^{2} = 0 \Rightarrow x = 4, x = 4$

Thus, both the roots of the given equation are equal and are equal to 4.

(ii) We have,

$x^{2} + 14 x - 32 = 0$

$\Rightarrow x^{2} + 16 x - 2 x - 32 = 0$

$\Rightarrow x (x + 16) - 2 (x + 16) = 0$

$\Rightarrow (x + 16) (x - 2) = 0 \Rightarrow x = - 16, x = 2$

$∴$ Roots are -16 and 2

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