# How do you use the discriminant to determine the nature of the roots for #4x^2 + 15x + 10 = 0#?

##### 1 Answer

#### Answer:

So

#### Explanation:

with

The discriminant is given by the formula:

This is positive, but not a perfect square. So the quadratic equation has two distinct irrational real roots.

The various possible cases (assuming that the quadratic has rational coefficients) are as follows: