Question

Factorise

x² + 3x - (a² + a - 2) = 0 ​

Answer 1

Here we have a quadratic equation and there's another quadratic equation in that.

x² + 3x - (a² + a - 2) = 0

First of all solve, a² + a - 2 = a² + 2a - a - 2 = a(a+2)-(a+2) = (a-1)(a+2)

Now,the equation we need to solve is

x² + 3x - {(a-1)(a+2)} = 0

So, Here it's little difficult to split the middle term otherwise it's quite easy.

So just use error and trial

(a+2)-(a-1) = 3 and also satisfy (a+2)(a-1)

So, after factorisation,

x² + 3x - {(a-1)(a+2)} = 0

=x² + {(a+2)-(a-1)}x- {(a-1)(a+2)} = 0

Let (a+2)=m and (a-1) =n

=x² + mx - nx - mn = 0

Solve by taking m and n common.

=x(x+m) - n(x+n)

=(x-n)(x+m)

So, its roots are x= n and x= - m

Replace the values of m and n

x= n = (a-1)

x= - m = - (a+2)

So, x= (a-1) or -(a+2)

My jaan, Hope you have understood.

❤️