Question
If the roots of the equation qx2 + px + q = 0 where p, q are real, are complex, then the roots of the equation x2 - 4qx + p2 = 0 are
Answer: Option A
:
A
The given equations are
qx2 + px + q = 0 ........(i)
andx2 - 4qx + p2 = 0 ........(ii)
Roots of (i) are complex, therefore p2−4q2 < 0
Now discriminant of (ii) is
16q2−4p2=−4(p2−4q2) > 0
Hence, roots are realand unequal.
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:
A
The given equations are
qx2 + px + q = 0 ........(i)
andx2 - 4qx + p2 = 0 ........(ii)
Roots of (i) are complex, therefore p2−4q2 < 0
Now discriminant of (ii) is
16q2−4p2=−4(p2−4q2) > 0
Hence, roots are realand unequal.
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