Question

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

• A. Real and unequal
• B. Imaginary
• C. Real and equal
• 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)

If the roots of the equation $a{x}^2+bx+c=0$ are complex, then $b^2-4ac<0$

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

Now discriminant of (ii) is

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

As $(p^2-4q^2)<0$, $-4(p^2-4q^2)>0$

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

Hence, roots are real and unequal.