Question

Find the roots of the equation a(x^2 + 1)-(a^2+ 1)x = 0, where a does not 0​

Answer 1

Answer:

$a( {x}^{2} + 1) - ( {a}^{2} + 1)x = 0 \\ on \: simplifying \: we \: get \: \\ a {x}^{2} - {a}^{2}x - x + a = 0 \\ ax(x - a) - 1(x - a) = 0 \\ (x - a)(ax - 1) = 0 \\ x - a = 0 \: or \: ax - 1 = 0 \\ x = a \: or \: x = \frac{1}{a} \\ therefore \: roots \: of \: the \: given \\ \: quadratic \: equation \: are \\ \: a \: and \: \frac{1}{a}$