Question

If the roots of the equation $a{x}^2+x+b=0$ are real and different, then the roots of the equation $x^2-4\sqrt{ab}x+1=0$ will be

• A. Rational
• B. Irrational
• C. Real
• D. Imaginary

Answer 1

The correct option is D Imaginary

Roots of the equation $a{x}^2+x+b=0$ are real and different.
$\Rightarrow D=B^2-4AC>0$
$\Rightarrow 1-4ab>0$
$\therefore 4ab-1<0$ ------(1)
$x^2-4\sqrt{ab}x+1=0$
$D=B^2-4AC=16ab-4=4(4ab-1)<0$ (from (1))
$\therefore$ Roots are imaginary.
Hence, option D.