Question

Write the nature of roots of quadratic equation 4x²+6x+3=0

Answer 1

Answer:

We know that

D=b^2-4ac

=(6)^2-4×4×3

=36-48

=-12

hence there is no real root

Answer 2

The nature of roots of quadratic equation 4x²+6x+3=0 is, imaginary.

Given: The quadratic equation is, 4x²+6x+3=0

To find The nature of the roots.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to determine the nature of roots)

First of all, we have to calculate the value of the discriminant.

If, a quadratic equation is :

ax²+bx+c = 0

Then, its discriminant = b²-4ac

By, comparing the given quadratic equation 4x²+6x+3=0 with the standard form of quadratic equation (i.e. ax²+bx+c = 0), we get :

• a = 4
• b = 6
• c = 3

So, discriminant will be :

= b²-4ac

= (6)²- (4 × 4 × 3)

= 36 - 48

= -12

Now,

The discriminant is less than zero. (12 < 0)

So, the nature of the roots will be :

= imaginary (i.e. no real roots)

Hence, the nature of roots of quadratic equation 4x²+6x+3=0 is, imaginary.