Question

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

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

Answer 1

The correct option is D Imaginary

Roots of first equation are real and distinct

$\Rightarrow 1\ge 4ab\to ab\le 1/4$

Descriminant of second equation =$16ab-4$

$ab\le 1/4\to 16ab\le 4\to 16ab-4\le 0$

$\therefore$descriminant of the second equation is less than zero

Therefore roots of second equation are imaginary