Question

If one root is square of the other root of the equation `x^2+p x+q=0` , then the relation between `pa n dq` is (2004, 1M) `p^3-(3p-1)q+q^2=0` `p^3-q(3p+1)+q^2=0` `p^3+q(3p-1)+q^2=0` `p^3+q(3p+1)+q^2=0`
A. `p^(3)-q(3p-1)+q^(2)=0`
B. `p^(3)-q(3p+1)+q^(2)=0`
C. `p^(3)+q(3p-1)+q^(2)=0`
D. `p^(3)+q(3p+1)+q^(2)=0`

Answer 1

Correct Answer - A
Let the roots of `x^(2)+px+q=0` be `alphaand alpha^(2).`
`impliesalpha+alpha^(2)=-pand alpha^(3)=q`
`impliesalpha(alpha+1)=-p`
`impliesalpha^(3){alpha^(3)+1+3alpha(alpha+1)}=-p^(3)["cubing both sides"]`
`impliesq(q+1-3p)=-p^(3)`
`impliesp^(3)-(3p-1)q+q^(2)=0`