Answer :
Certainly! Let's find the discriminant of the quadratic equation [tex]\(x^2 - 9x - 2 = 0\)[/tex].
The discriminant of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex] is found using the formula:
[tex]\[
D = b^2 - 4ac
\][/tex]
Here, the coefficients are:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -9\)[/tex]
- [tex]\(c = -2\)[/tex]
Now, substitute these values into the formula:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-9)^2 = 81
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 1 \times (-2) = -8
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex] to find the discriminant:
[tex]\[
81 - (-8) = 81 + 8 = 89
\][/tex]
Therefore, the discriminant of the equation [tex]\(x^2 - 9x - 2 = 0\)[/tex] is [tex]\(89\)[/tex].
The discriminant of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex] is found using the formula:
[tex]\[
D = b^2 - 4ac
\][/tex]
Here, the coefficients are:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -9\)[/tex]
- [tex]\(c = -2\)[/tex]
Now, substitute these values into the formula:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
(-9)^2 = 81
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4 \times 1 \times (-2) = -8
\][/tex]
3. Subtract [tex]\(4ac\)[/tex] from [tex]\(b^2\)[/tex] to find the discriminant:
[tex]\[
81 - (-8) = 81 + 8 = 89
\][/tex]
Therefore, the discriminant of the equation [tex]\(x^2 - 9x - 2 = 0\)[/tex] is [tex]\(89\)[/tex].
