Question

Question 8
The quadratic equation $2x^2-\sqrt{5}x+1=0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

Answer 1

Option C

The discriminant D is used to find the nature of roots for any quadratic equation.

D = $b^2-4ac$

If D < 0, the roots of the quadratic equation are not real and imaginary.

If D = 0, both the roots of the quadratic equation are same.

If D>0, roots of the quadratic equation are are real and distinct.

So given equation is $2x^2-\sqrt{5}x+1=0$

On comparing with $a{x}^2+bx+c=0$, we get

a= 2 , b = $-\sqrt{5}$, c = 1

D = $(-\sqrt{5}{)}^2-4(2\left)\right(1)$ = 5 - 8 = -3 < 0

So D < 0 , the roots are of the given equation doesnt have real roots.