Question

Find the discriminant of the quadratic equation and indicate the number of roots: (3x^2)+2x+1=0

Answer 1

Answer:

This expression has no roots.

Step-by-step explanation:

Using the discriminant: b² - 4ac, we get:

2² - 4 × 3 × 1

= 4 - 12

= -8

So this equation has no real solutions.  Let's prove that by trying to solve for x:

3x² + 2x + 1 = 0

9x² + 6x + 3 = 0

9x² + 6x + 1 = -2

(3x + 1)² = -2

3x + 1 = i√2

3x = -1 ± i√2

x = (-1 ± i√2) / 3

The only solutions available then are indeed complex.

Answer 2

Discriminant: -8

There are no roots

To find the discriminant, we use: $b^{2} -4ac$

In this quadratic equation:

b = 2

a = 3

c = 1

Plug the values in: $2^{2} - 4(3*1)$ = -8

The discriminant is -8.

Since -8 < 0, there are no roots.