Question 8
The quadratic equation 2x2−√5x+1=0 has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots
Option C
The discriminant D is used to find the nature of roots for any quadratic equation.
D = b2 − 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 2x2−√5x+1=0
On comparing with ax2+bx+c=0, we get
a= 2 , b = −√5, c = 1
D = (−√5)2 − 4(2)(1) = 5 - 8 = -3 < 0
So D < 0 , the roots are of the given equation doesnt have real roots.