Question

If the roots of the equation q$x^2$ + p$x$ + q = 0 where p, q are real, are complex, then the roots of the equation $x^2$ - 4q$x$ + $p^2$ = 0 are

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

Answer 1

The correct option is A

Real and unequal

The given equations are

q$x^2$ + p$x$ + q = 0 ........(i)

and $x^2$ - 4q$x$ + $p^2$ = 0 ........(ii)

Roots of (i) are complex, therefore $p^2-4q^2$ < 0

Now discriminant of (ii) is

$16q^2-4p^2=-4(p^2-4q^2)$ > 0

Hence, roots are real and unequal.