Question

What is quadratic equation of a(x^2+1)-x(a^2+1)?

Answer 1

Answer:

Given, quadratic equation is

=> a(x2 + 1) - x(a2 + 1) = 0

=> ax2 + a - xa2 - x = 0

=> ax2 - (a2 + 1)x + a = 0

Using quadratic formula, we get

=> x = [-{-(a2 + 1)} ± √{(a2 + 1)2 - 4 * a * a}]/2a

=> x = [(a2 + 1) ± √{a4 + 1 + 2a2 - 4 * a2 }]/2a

=> x = [(a2 + 1) ± √{a4 + 1 - 2a2 }]/2a

=> x = [(a2 + 1) ± √{(a2 - 1)2 }]/2a

=> x = [(a2 + 1) ± (a2 - 1)]/2a

=> x = [(a2 + 1) + (a2 - 1)]/2a and x = [(a2 + 1) - (a2 - 1)]/2a

=> x = 2a2 /2a and x = 2/2a

=> x = a, 1/a

So, the roots are a and 1/a

I hope it helps you

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