Question 1(i)
Find the roots of the following quadratic equations by factorisation:
(i) $x^{2} - 3 x - 10 = 0$

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Solution

(i) $x^{2} - 3 x - 10 = x^{2} - 5 x + 2 x - 10 = x (x - 5) + 2 (x - 5) = (x - 5) (x + 2)$
Roots of this equation are the values for which $(x - 5) (x + 2) = 0$
$∴ x - 5 = 0 o r x + 2 = 0$
$\Rightarrow x = 5 o r x = - 2$

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Question 1 (iv)

Find the roots of the quadratic equations by using the quadratic formula in the following question.

$- x^{2} + 7 x - 10 = 0$

2 x^{2} - 7 x + 3 = 0

(x^{2} + 3 x + 2)^{2} - 8 (x^{2} + 3 x) - 4 = 0

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