The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is:(a) No real roots (b) 2 equal real roots(c) 2 distinct real roots (d) More than 2 real roots

To determine the nature of the roots of the quadratic equation 9x^2 - 6x - 2 = 0, we can use the discriminant formula. The discriminant (D) is given by the equation D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 9, b = -6, and c = -2. Substituting these values into the discriminant formula, we have D = (-6)^2 - 4(9)(-2).

Simplifying further, D = 36 + 72 = 108.

Now, let's analyze the value of the discriminant:

• If D > 0, then the quadratic equation has two distinct real roots.
• If D = 0, then the quadratic equation has two equal real roots.
• If D < 0, then the quadratic equation has no real roots.

In our case, D = 108, which is greater than 0. Therefore, the nature of the roots of the quadratic equation 9x^2 - 6x - 2 = 0 is (c) 2 distinct real roots.