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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].
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].
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