High School

What is the discriminant of the quadratic equation [tex]6x^2 - x - 6 = 0[/tex]?

A. [tex]-145[/tex]
B. [tex]143[/tex]
C. [tex]145[/tex]
D. [tex]-143[/tex]

Answer :

To find the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex], we use the formula for the discriminant, which is [tex]\(b^2 - 4ac\)[/tex].

Here are the steps:

1. Identify the coefficients in the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex]:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -1\)[/tex]
- [tex]\(c = -6\)[/tex]

2. Plug the coefficients into the discriminant formula:
[tex]\[
\text{Discriminant} = b^2 - 4ac
\][/tex]

3. Substitute the values:
[tex]\[
\text{Discriminant} = (-1)^2 - 4 \times 6 \times (-6)
\][/tex]

4. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]

5. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 6 \times (-6) = -144
\][/tex]

6. Put it all together:
[tex]\[
\text{Discriminant} = 1 - (-144) = 1 + 144 = 145
\][/tex]

So, the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex] is [tex]\(145\)[/tex].