Answer :
To find the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex], we first identify the coefficients in the standard form of a quadratic equation, which is [tex]\(ax^2 + bx + c = 0\)[/tex].
Here, the coefficients are:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -1\)[/tex]
- [tex]\(c = -6\)[/tex]
The discriminant of a quadratic equation is calculated using the formula:
[tex]\[
D = b^2 - 4ac
\][/tex]
Let's calculate it step-by-step:
1. Square the coefficient [tex]\(b\)[/tex]:
[tex]\[
b^2 = (-1)^2 = 1
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4ac = 4 \times 6 \times (-6) = 4 \times -36 = -144
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex]:
[tex]\[
D = 1 - (-144) = 1 + 144 = 145
\][/tex]
Thus, the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex] is [tex]\(\boxed{145}\)[/tex].
Here, the coefficients are:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -1\)[/tex]
- [tex]\(c = -6\)[/tex]
The discriminant of a quadratic equation is calculated using the formula:
[tex]\[
D = b^2 - 4ac
\][/tex]
Let's calculate it step-by-step:
1. Square the coefficient [tex]\(b\)[/tex]:
[tex]\[
b^2 = (-1)^2 = 1
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4ac = 4 \times 6 \times (-6) = 4 \times -36 = -144
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex]:
[tex]\[
D = 1 - (-144) = 1 + 144 = 145
\][/tex]
Thus, the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex] is [tex]\(\boxed{145}\)[/tex].
