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Answer :
Sure! Let's find the discriminant of the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex].
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are coefficients.
In this equation:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -1\)[/tex]
- [tex]\(c = -6\)[/tex]
The formula to find the discriminant ([tex]\(D\)[/tex]) of a quadratic equation is:
[tex]\[ D = b^2 - 4ac \][/tex]
Now, let's substitute the values into the formula:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 6 \times (-6) = 4 \times 6 \times -6 = -144
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex]:
[tex]\[
1 - (-144) = 1 + 144 = 145
\][/tex]
So, the discriminant for the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex] is [tex]\(145\)[/tex].
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are coefficients.
In this equation:
- [tex]\(a = 6\)[/tex]
- [tex]\(b = -1\)[/tex]
- [tex]\(c = -6\)[/tex]
The formula to find the discriminant ([tex]\(D\)[/tex]) of a quadratic equation is:
[tex]\[ D = b^2 - 4ac \][/tex]
Now, let's substitute the values into the formula:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 6 \times (-6) = 4 \times 6 \times -6 = -144
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex]:
[tex]\[
1 - (-144) = 1 + 144 = 145
\][/tex]
So, the discriminant for the quadratic equation [tex]\(6x^2 - x - 6 = 0\)[/tex] is [tex]\(145\)[/tex].
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