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Zeroes of a Polynomial

Solve the fol...

Question

Solve the following quadratic equations by factorisation :
$(i) x^{2} + 3 x - 40 = 0 (i i) 12 x^{2} - 17 x + 5 = 0 (i i i) 4 x^{2} + 9 = 12 x (i v) 2 x^{2} - 11 x + 5 = 0$

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Solution

(1) $x^{2} + 3 x - 40 = 0$
$x^{2} + 8 x - 5 x - 40 = 0$
$x (x + 8) - 5 (x + 8) = 0$
$(x - 5) (x + 8) = 0$

$(2) 12 x^{2} - 17 x + 5 = 0$
$12 x^{2} - 12 x - 5 x + 5 = 0$
$12 x (x - 1) - 5 (x - 1) = 0$
$(12 x - 5) (x - 1) = 0$

(3) $4 x^{2} - 12 x + 9 = 0$
$4 x^{2} - 6 x - 6 x + 9 = 0$
$2 x (2 x - 3) - 3 (2 x - 3) = 0$
$(2 x - 3)^{2} = 0$

(4) $2 x^{2} - 11 x + 5 = 0$
$2 x^{2} - 10 x - x + 5 = 0$
$2 x (x - 5) - 1 (x - 5) = 0$
$(2 x - 1) (x - 5) = 0$

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