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Question

Question 8
The quadratic equation 2x25x+1=0 has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots


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Solution

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 2x25x+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.


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