Question

Factorise the polynomial: 2x - 3x2 - 11x + 6​

Answer 1

We have,

$\quad \: 2x - 3 {x}^{2} - 11x + 6 \\ \\ = - 3 {x}^{2} + 2x - 11x + 6 \\ \\ = - 3 {x}^{2} - 9x + 6$

This equation is of the form : $\underline{ \boxed{a {x}^{2} + bx + c}}$
Here,
⚪a = - 3
⚪b = - 9
⚪c = 6

let ax² + bx + c = 0

Then,
discriminant, D
$= {b}^{2} - 4ac \\ \\ = {( - 9)}^{2} - 4( - 3)(6) \\ \\ = 81 + 72 \\ \\ = 153 \implies153 > 0$
Thus, the value of x is real and distinct.

Thus,
$x = \frac{ - b \pm \sqrt{D} }{2a}$
Therefore,
$x = \frac{9 + \sqrt{153} }{ - 6} \: \boxed{or} \: \frac{9 - \sqrt{153} }{ - 6}$
Hence,

$\underline{\boxed{ - 3 {x}^{2} - 9x + 6 = \left(x + \frac{9 + \sqrt{153} }{6} \right) \left(x + \frac{9 - \sqrt{153} }{6} \right) }}$

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$