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

Answer: last option

Step-by-step 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.

Answer 2

ANSWER

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.