Question

6x^2+5x-6 factorise polynomial​

Answer 1

Solution:-

We have equation

$\rm \implies \: 6 {x}^{2} + 5x - 6 = 0$

Now Split into middle term

$\rm \implies \: 6 {x}^{2} + 9x - 4x - 6 = 0$

$\rm \implies \: 3x(2x + 3) - 2(2x + 3) = 0$

$\rm \implies \: (3x - 2)(2x + 3) = 0$

$\rm \implies \: 3x - 2 = 0 \: \: and \: \: 2x + 3 = 0$

$\rm \implies \: 3x = 2 \: \: and \: 2x = - 3$

$\rm \implies \: x = \dfrac{2}{3} \: \: and \: \: x = \dfrac{ - 3}{2}$

Method :-2

Using quadratic formula

We have

$\rm \implies \: 6 {x}^{2} + 5x - 6 = 0$

$\rm \implies \: a = 6,b = 5 \: \: and \: \: c = - 6$

Quadratic formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

Put the value on formula

$\rm \implies \: x = \dfrac{ - 5 \pm \sqrt{ {5}^{2} - 4 \times 6 \times - 6 } }{2 \times 6}$

$\rm \implies \: x = \dfrac{ - 5 \pm \sqrt{25 + 144} }{12}$

$\rm \implies \: x = \dfrac{ - 5 \pm \sqrt{169} }{12}$

$\rm \implies \: x = \dfrac{ - 5 \pm13}{12}$

$\rm \implies \: x = \dfrac{ - 5 + 13}{12} \: \: and \: \dfrac{ - 5 - 13}{12}$

$\rm \implies \: x = \dfrac{8}{12} \: \: and \: \dfrac{ - 18}{12}$

$\rm \to \: x = \dfrac{2}{3} \: \: and \: \: \dfrac{ - 3}{2}$