Question

solve the quadratic equation by factorisation ​

Answer 1

Solution:

$6m {}^{2} + m - 15 = 0 \\ \\ = > 6m {}^{2} + 10m - 9m - 15 = 0 \\ \\ = > 2m(3m + 5) - 3(3m + 5) = 0 \\ \\ = > (2m - 3)(3m + 5) = 0 \\ \\ = > 2m - 3 = 0 \: \: or \: \: 3m + 5 = 0 \\ \\ = > 2m = 3 \: \: or \: \: 3m = - 5 \\ \\ = > m = \frac{3}{2} \: \: or \: \: \frac{ - 5}{3}$

3/2 and -5/3 are the zeros of the given quadratic equations.

Splitting the middle term should be:

-15×6=-90

and we need to split it such that it's factors when subtracted give the answer 1.

90=9×10

On subtraction,

10-9=1

We obtain the result required and split it accordance with the equation

Answer 2

6m^2+m-15=0

6m^2-9m+10m-15=0

3m(2m-3)+5(2m-3)=0

(3m+5)(2m-3)=0

3m+5=0 & 2m-3=0

m=-5/3. &m=3/2