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Question

If the roots of the equation qx2+px+q=0 where p, q are real, be complex, then the roots of the equation x24qx+p2=0 are


A

Real and unequal

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B

Real and equal

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C

Imaginary

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D

None of these

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Solution

The correct option is A

Real and unequal


The given equations are

qx2 + px + q = 0 ....(i)

and~x2 - 4qx + p2 = 0 ......(ii)

Roots of (i) are complex, therefore p24q2 < 0

Now discrimninant of (ii) is 16q24p2=4(p24q2) > 0

Hence, roots are real and unequal


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