The equation formed by multiplying each root of `ax^(2) + bx+ c = 0" by "2 " is "x^(2) = 36x + 24 =0`
If the roots of a quadratic equation `ax^(2)+ bx+ c=0 " are "alpha and beta,` then the quadratic equation having roots `alpha and beta` is

Options

A. `x^(2) - (b^(2)-2ac) x + c= 0`
B. `a^(2)x^(2)- (b^(2) - 2ac) x + c =0`
C. `ax^(2) - ( b^(2) - 2ac) x + c^(2) =0`
D. `a^(2) x^(2) - ( b^(2) - 2ac) x + c^(2) = 0`

Answer

D

Explanation

Quadratic equation is given by
`x^(2) -"(sum or roots)" x + " ( product of roots) " = 0 `
`:. " Required equation is " x^(2) - x ( alpha^(2) + beta^(2) ) + ( alpha beta )^(2) = 0 ``rArr - x [ ( alpha + beta)^(2)-2 alpha beta ] + ( alpha beta)^(2) = 0 `
`rArr x^(2) - x (b^(2)/a^(2) - (2c)/a)+ c^(2)/a^(2)= 0 `
`rArr a^(2) x^(2) - x(b^(2) - 2ac) + c^(2)= 0 `