Question

Solve the following quadratic equations by factorization: a(x²+1)-x(a²+1)=0

Answer 1

SOLUTION :  

Given : a(x² + 1) - x(a² + 1) = 0

ax² + a - a²x - x = 0

ax² - a²x - x + a = 0

ax(x - a ) - 1(x - a) = 0

(ax - 1) (x - a) = 0

(ax - 1) = 0  or  (x - a) = 0

[Equate each factor to zero]

ax = 1  or  x = a  

x = 1/a  or  x = a  

Hence, the roots of the quadratic equation a(x² + 1) - x(a² + 1) = 0  are  1/a  &  a .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Begin by writing the given quadratic equation,

a(x² + 1) - x(a² + 1) = 0

Secondly, solve the given equation,

ax² + a - a²x - x = 0

Rearrange the given equations so that the pairs are kept together (It helps the examiner to better understand your calculation),

ax² - a²x - x + a = 0

Taking out common factors,

ax(x - a ) - 1(x - a) = 0

One again taking out common factors,

(ax - 1) (x - a) = 0

Following the zero product rule,

(ax - 1) = 0 OR (x - a) = 0
=> ax = 1 OR x = a
=> x = 1/a OR x = a

Therefore,

The roots of the given quadratic equation are 1/a and a.