Math, asked by money3323, 8 months ago

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

Answers

Answered by Mihir1001
18
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
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