InterviewSolution
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InterviewSolution
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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` |
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Answer» 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` |
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