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Question

If one root is square of the other root of the equation x2+px+q=0, then the relation between pandq is


A

p3(3p1)q+q2=0

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B

p3q(3p+1)+q2=0

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C

p3+q(3p-1)+q2=0

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D

p3-q(3p-1)+q2=0

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Solution

The correct option is A

p3(3p1)q+q2=0


Explanation for the correct option.

Let the one root of the given equation be α then the other root will be α2.

Now, we know that the sum of these roots will be equal to -p and their product will be equal to q. From this we construct two equations,

α+α2=-p1

α3=q2

Now, in equation 1, apply the cube on both the sides,

α2+α3=-p3αα+13=-p3

Apply the algebraic identity (a+b)3=a3+b3+3ab(a+b), then

-p3=a3a3+1+3aa+1

Apply the value of a3 from equation 2,

-p3=qq+1+3-pp3+q2+q-3pq=0p3-3p-1q+q2=0

Hence, the correct option is (A).


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