Q. 244.3( 3 Votes )

# If α and β are the roots of ax2 + bx + c = 0, then one of the quadratic equations whose roots are isA. ax2 + bx + c = 0B. bx2 + ax + c = 0C. cx2 + bx + a = 0D. cx2 + ax + b = 0

Answer :

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)

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