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: …

Question

asked Oct 20, 2020 116k views

2 Answers

Tommaso Taruffi · Answer 1 · 2020-10-21T19:10:45+0000

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.

Adrion · Answer 2 · 2020-10-26T20:37:43+0000

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.