If α and β are the roots of ax² + bx + c = 0, then one of the quadratic equations whose roots are is

Given: and are roots of

Required:- Quadratic equation with roots and

Sum of roots of given quadratic equation =

∴ = -eq(1)

Product of roots of given quadratic equation =

∴ = -eq(2)

Sum of roots of required quadratic equation =

Product of roots of required quadratic equation =

Here,

Dividing eq(1) by eq(2) we get,

∴ Sum of roots of the required quadratic equation =

Again by making the reciprocal of eq(2), we get

∴ Product of roots of the required quadratic equation =

We know that, when roots of the quadratic equation are known, we can calculate the quadratic equation as:

x²-(sum of roots)x + (product of roots) = 0

∴ Required quadratic equation: x² –() + () = 0

⇒ = 0

⇒ cx² + bx + a = 0

∴ Required quadratic equation is: cx² + bx + a = 0

∴ Correct option is -Option(C)