Question

The roots of the equation a(x2 + 1) - x(a2 + 1) = 0 is​

Answer 1

Answer:

An Quadratic equations,

$\bf \implies \:a( {x}^{2} + 1) - x( {a}^{2} + 1) = 0 \\ \\ \bf \implies \: {ax}^{2} + a - x( {a}^{2} +1 ) = 0 \\ \\ \bf \implies \: {ax}^{2} - ( {a}^{2} + 1)x + a = 0$

Here,

• A = a
• B = -(a²+1)
• C= a

Splitting the middle term!!!

$\bf \implies \: {ax}^{2} - {a}^{2} x - x + a = 0 \\ \\ \bf \implies \:ax(x - a) - 1(x - a) = 0 \\ \\ \bf \implies \:(ax - 1)(x - a) = 0 \\ \\ \bf \implies \:ax - 1 = 0 \: \: \: \: \: \: \: (or) \: \: \: \: \: \: x - a = 0 \\ \\ \bf \implies \:x = \frac{1}{a} \: \: \: \: (or) \: \: \: \: a$

Roots of the Quadratic equations is 1/a or a!!!!

Verification:-

Sum of zeroes = -b/a = 1/a+a = -(-(a²+1))/a

•°• (1+ a²)/a = (1+a²)/a

Products of zeroes = c/a = 1/a×a =a/a

•°• 1 = 1

Hence verified!!!!