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What is the nature of the roots of 3x23x^23x2​– 6xxx​ + 5 = 0?
Question

What is the nature of the roots of 3x23x^2​– 6xx​ + 5 = 0?

A.

The roots are real and equal.

B.

The roots are real and more than 2.

C.

The roots are real and distinct.

D.

There are no real roots.

Correct option is D

Given:

3x23x^2-6xx +  5 = 0

Formula Used for quadratic equation ax2+bx+c=0ax^2+bx+c=0

Discriminant (D) = b24acb^2-4ac

Solution: 

From the equation:

a=3,b=6,c=5a=3, b=-6,c=5 

Putting values in Discriminant formula:

D = (62-6^2) - 4(3)(5)

D = 36 - 60

D = -24

If the value of D<0 : Two complex root.

So there is no real root.

Thus the correct answer is (D).

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