Verified answer

The discriminant of a polynomial is described as 0 = b^2 - 4ac (you may recognize that from the numerator of the quadratic formula; it's the part under the square root).

In this case, add 1 to both sides of the equation so you get 9x^2 + 6x + 1 = 0

Now it's in the proper form to use the discriminant.

Note that when solving, there are 3 possibilities; x can be >0, x can be <0, or x can be =0.

If

• x < 0, The equation has no real roots.

• x = 0, The equation has 1 real root

• x > 0, The equation has 2 real roots

b^2 - 4ac = x

6^2 - 4(9)(1) = x

36 - 36 = x

0 = x

Since x = 0, the equation of 9x^2 + 6x + 1 = 0 has 1 real root (one x-intercept).

Hope this helps!