Question

Factorice 6x square+5x-6

Answer 1

Answer:

Factorisation of given equation $(6x^{2}+5x-6)$ is $(2x+3)(3x-2).$

Step-by-step explanation:

As per the given information in equation.

Given,

$6x^{2} +5x-6$

We have to factorise the equation,

$6^{2} + 9x-4x-6\\3x(2x+3)-2(2x+3)\\(2x+3)(3x-2)$

Hence,

Factorisation of given equation $6x^{2}+5x-6$ is $(2x+3)(3x-2)$.

Answer 2

The roots of  6x²+5x-6  are  $\alpha =\frac{2}{3}$  and  $\beta =\frac{-3}{2}$

Explanation:

Given:

6x²+5x-6

To find:

The roots of the equation

Formula:

$\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Solution:

==> 6x²+5x-6

==> a = coefficient of x

==> b = Coefficient of x

==> c = constant

==> a = 6

==> b = 5

==> c = -6

==> Apply the values in the formula

==> $\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

==> $\alpha =\frac{-5+\sqrt{5^{2}-4(6)(-6) } }{2(6)}$

==> $\alpha =\frac{-5+\sqrt{25-4(-36) } }{2(6)}$

==> $\alpha =\frac{-5+\sqrt{25+144 } }{12}$

==> $\alpha =\frac{-5+\sqrt{169} }{12}$

==> $\alpha =\frac{-5+13}{12}$

==> $\alpha =\frac{8}{12}$

==> $\alpha =\frac{8}{12}$

==> $\alpha =\frac{4}{6}$

==> $\alpha =\frac{2}{3}$

==> $\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

==> $\beta =\frac{-5-\sqrt{5^{2}-4(6)(-6) } }{2(6)}$

==> $\beta =\frac{-5-\sqrt{25-4(-36) } }{2(6)}$

==> $\beta =\frac{-5-\sqrt{25+144 } }{12}$

==> $\beta =\frac{-5-\sqrt{169} }{12}$

==> $\beta =\frac{-5-13}{12}$

==> $\beta =\frac{-18}{12}$

==> $\beta =\frac{-9}{6}$

==> $\beta =\frac{-3}{2}$

The roots of  6x²+5x-6  are  $\alpha =\frac{2}{3}$  and  $\beta =\frac{-3}{2}$