Question

Find the root of quadratic equation
$2x {}^{2} + x - 6 = 0$
​

Answer 1

2x² + x - 6 = 0

By Middle Term Factorisation

⇒ 2x² + 4x - 3x - 6 = 0

Taking common

⇒ 2x ( x + 2 ) - 3 ( x + 2 ) = 0

⇒ ( 2x - 3 ) ( x + 2 ) = 0

Using Zero Product Rule

⇒ 2x - 3 = 0 and x + 2 = 0

⇒ x = 3 / 2 and x = - 2

Hence, $<b>the roots of the given quadratic equation are - 2 and 3 / 2.</b>$

Answer 2

$2 {x}^{2} + x - 6=0 \\ = 2 {x}^{2} + (4 - 3)x - 6=0 \\ = 2 {x }^{2} + 4x - 3x - 6=0 \\ = 2x(x + 2) - 3(x + 2)=0 \\ = (x + 2)(2x - 3)$
so
x+2=0
x=-2
and
2x-3=0
×=3/2

Hope it will help you...