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

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.

1; 35 is the ratio

step-by-step explanation: