Question

Step by step factorise ax²+(1+a²)x+a

Answer 1

Answer:-

$x = \dfrac{ - 1}{a} \: \: \: \: x = - a$

Given:-

$a {x}^{2} + (1 + {a}^{2} )x + a$

To find :-

It's factorization

Solution:-

$a {x}^{2} + (1 + {a}^{2} )x + a$

$a {x}^{2} + x + {a}^{2} x + a = 0$

$a {x}^{2} + {a}^{2} x + x + a = 0$

Taking ax and 1 as common,

We get,

$ax(x + a) + 1(x + a) = 0$

$(ax + 1)(x + a) = 0$

$(ax + 1) = 0 \: \:$

$(x + a) = 0$

$ax + 1 = 0$

$x = \dfrac{ - 1}{a}$

or,

$x = - a$

hence, the solution is

$x = \dfrac{ - 1}{a} \: \: \: \: x = - a$