Question

Use the discriminant to describe the roots of each equation. Then select the best description. 6x2 + 13x + 6 = 0

double root
real and rational roots
real and irrational roots
non-real roots

Answer 1

A. double root

Explanation:

Answer 2

The quadratic formula for a quadratic of the form ax^2+bx+c is

x=(-b±
`√(b^2-4ac)`)/(4a)

The discriminant is the part under the radical sign.

There are three possibilities for the discriminant and the roots that the formula will produce.

The discriminant is positive: There will be two real roots.

The discriminant is negative: There will be no REAL root, however there will be two imaginary roots

The discriminant is zero. There will be one real root.

In this example. b^2-4ac=169-144=25

So there will be two real roots as it is greater than zero.