If the roots of the equation a x2+x+b=0 be real and unequal where a, b ∈ R, then the roots of the equation x2-4 √a b x+1=0 will be

Question

If the roots of the equation a x2+x+b=0 be real and unequal where a, b ∈ R, then the roots of the equation x2-4 √a b x+1=0 will be (A) Rational (B) Irrational (C) Real (D) Imaginary

Tardigrade Admin · Accepted Answer

a x2+x+b=0 roots are real and unequal so 1-4 a b>0 .......(i) x2-4 √a b x+1=0 D=16 a b-4=4[4 a b-1]<0 text from (i) So roots are imaginary

Q. If the roots of the equation $a x^{2} + x + b = 0$ be real and unequal where $a, b \in R$ , then the roots of the equation $x^{2} - 4 ab x + 1 = 0$ will be

Rational

Irrational

Real

Imaginary

$a x^{2} + x + b = 0$
roots are real and unequal so $1 - 4 ab > 0$ .......(i)
$x^{2} - 4 ab x + 1 = 0$
$D = 16 ab - 4 = 4 [4 ab - 1] < 0 {from (i)}$
So roots are imaginary

Q. If the roots of the equation ax2+x+b=0 be real and unequal where a,b∈R, then the roots of the equation x2−4ab​x+1=0 will be