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Question

If the roots of the equation qx2 + px + q = 0 are complex, where p, q are real. Then the roots of the equation x2 - 4qx + p2 = 0 are

A
Real and unequal
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B
Imaginary
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C
Real and equal
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D
nothing can be said in particular
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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)

If the roots of the equation ax2+bx+c=0 are complex, then b24ac<0

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

Now discriminant of (ii) is

16q24p2=4(p24q2)

As (p24q2)<0, 4(p24q2)>0

As the value of the discriminant is positive, roots are real and unequal.

Hence, roots are real and unequal.


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