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 is
A. ax2 + bx + c = 0

B. bx2 + ax + c = 0

C. cx2 + bx + a = 0

D. 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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