# If a quadratic equation with real coefficients has a discriminant of 10, then what type of roots...

## Question:

If a quadratic equation with real coefficients has a discriminant of 10, then what type of roots does it have?

A. 2 real, rational roots

B. 2 real, irrational roots

C. 1 real, irrational root

D. 2 imaginary roots

The quadratic formula provides the solution to a quadratic equation of the general form {eq}ax^2 + bx + c =0 {/eq} and it has the form of {eq}x = \dfrac{-b \pm \sqrt{b -4ac}}{2a} {/eq}. Where {eq}a, b, {/eq} and {eq}c {/eq} are constants and {eq}a \neq 0 {/eq}. The term under the radical sign is also called the discriminant

The answer is B. 2 real, irrational roots

Using the value of the discriminant in the quadratic formula to determine the kinds of solutions it offers:

{eq}x = \dfrac{-b \pm \sqrt{b -4ac}}{2a} \\ x = \dfrac{-b \pm \sqrt{10}}{2a} {/eq}

Upon inspection, the discriminant cannot be written any other way except as a radical since it is not a perfect square. Hence, there are 2 real and irrational roots.