Question

Find the roots of the quadratic equation: a (a2 + b2) x2 + b2x – a = 0

Answer 1

The roots of the equation are $x=\frac{-b^2+\sqrt{4a^4+5b^4}}{2a(a^2+b^2)},\frac{-b^2-\sqrt{4a^4+5b^4}}{2a(a^2+b^2)}$

Step-by-step explanation:

Given : Equation $a(a^2+b^2)x^2+b^2 x-a=0$

To find : The roots of the quadratic equation ?

Solution :

The quadratic equation  $Ax^2+Bx+C=0$ solution is given by $x=\frac{-B\pm\sqrt{B^2-4AC}}{2A}$

On comparing with equation,

$A=a(a^2+b^2), B=b^2$ and C=-a

Substitute the value,

$x=\frac{-b^2\pm\sqrt{(b^2)^2-4(a(a^2+b^2))(-a)}}{2a(a^2+b^2)}$

$x=\frac{-b^2\pm\sqrt{b^4+4a^2(a^2+b^2)}}{2a(a^2+b^2)}$

$x=\frac{-b^2\pm\sqrt{b^4+4a^4+4b^4}}{2a(a^2+b^2)}$

$x=\frac{-b^2\pm\sqrt{4a^4+5b^4}}{2a(a^2+b^2)}$

Therefore, the roots of the equation are $x=\frac{-b^2+\sqrt{4a^4+5b^4}}{2a(a^2+b^2)},\frac{-b^2-\sqrt{4a^4+5b^4}}{2a(a^2+b^2)}$

#Learn more

Find the roots of this quadratic equation.

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