Question

Use the discriminant to determine the number of real solutions to the quadratic equation. n^2 − n − 6 = 0 What is the number of real solutions? Select the correct answer below:

0
1
2

Answer 1

2

EXPLANATION

The given quadratic equation is

`{n}^(2) - n - 6 = 0`

Comparing to

`a{n}^(2) + b n + c = 0`

We have a=1, b=-1 and c=-6

The discriminant is given by the formula,

`D = {b}^(2) - 4ac`

Plug in the values to get,

`D = {( - 1)}^(2) - 4(1)( - 6)`

`D =1 + 24 = 25`

Since the discriminant is positive, the equation has two real roots.

Answer 2

Answer: last option

Explanation:

The formula to find the Discriminant is:

`D=b^2-4ac`

Given the quadratic equation
`n^2-n-6=0`, you can identify that:

`a=1\\b=-1\\c=-6`

Now, you can substitute values into the formula
`D=b^2-4ac`, then:

`D=b^2-4ac\\D=(1)^2-4(1)(-6)\\D=25`

As the Discriminant is greater than 0 (
`D>0`), then the quadratic equation
`n^2-n-6=0` has two distinct real solutions.