Question

Find the zeros of the polynomial bg factorisation method and verify the relation 3x2+4x-4

Answer 1

$3 {x}^{2} + 4x - 4 = 0 \\ 3 {x}^{2} + (6 - 2)x - 4 = 0 \\ 3 {x}^{2} + 6x - 2x - 4 = 0 \\ 3x(x + 2) - 2(x + 2) = 0 \\ (3x - 2)(x + 2) = 0 \\ \\ 3x - 2 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 2 = 0 \\ \: \: \: \: \: \: \: \: 3x = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 2 \\ \: \: \: \: \: \: \: \: \: \: x = \frac{2}{3}$

$.......verification.......$

$sum \: of \: zeros = \frac{ - b}{a} \\ \\ \: \: \: \: \: \: \: \: \frac{2}{3} + ( - 2) = \frac{ - 4}{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{2 - 6}{3} = \frac{ - 4}{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ - 4}{3} = \frac{ - 4}{3}$

$product \: of \: zeros \: = \frac{c}{a} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{2}{3} \times - 2 = \frac{ - 4}{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{ - 4}{3} = \frac{ - 4}{3}$
$hence \: verified...$

Answer 2

Question:-

Find the zeros of the polynomial bg factorisation method and verify the relation 3x²+4x-4

Solution:-

=> 3x² + 4x - 4

=> 3x² + 6x - 2x - 4

=> 3x ( x + 2 ) - 2 ( x + 2 )

=> ( 3x - 2 ) ( x + 2 )

let,

=> 3x - 2 = 0 or x + 2 = 0

=> 3x = 2 or x = - 2

=> x = 2/3 or x = - 2

i hope it helps you.