Answer :
To find the discriminant of the quadratic equation [tex]\(x^2 - 9x - 3 = 0\)[/tex], we will use the formula for the discriminant, which is:
[tex]\[ D = b^2 - 4ac \][/tex]
In this equation, the coefficients are:
- [tex]\( a = 1 \)[/tex] (the coefficient of [tex]\(x^2\)[/tex])
- [tex]\( b = -9 \)[/tex] (the coefficient of [tex]\(x\)[/tex])
- [tex]\( c = -3 \)[/tex] (the constant term)
Now, we will substitute these values into the discriminant formula:
1. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = (-9)^2 = 81
\][/tex]
2. Calculate [tex]\( 4ac \)[/tex]:
[tex]\[
4ac = 4 \times 1 \times (-3) = -12
\][/tex]
3. Substitute the calculated values into the discriminant formula:
[tex]\[
D = 81 - (-12) = 81 + 12 = 93
\][/tex]
Therefore, the discriminant of the quadratic equation [tex]\(x^2 - 9x - 3 = 0\)[/tex] is 93.
[tex]\[ D = b^2 - 4ac \][/tex]
In this equation, the coefficients are:
- [tex]\( a = 1 \)[/tex] (the coefficient of [tex]\(x^2\)[/tex])
- [tex]\( b = -9 \)[/tex] (the coefficient of [tex]\(x\)[/tex])
- [tex]\( c = -3 \)[/tex] (the constant term)
Now, we will substitute these values into the discriminant formula:
1. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = (-9)^2 = 81
\][/tex]
2. Calculate [tex]\( 4ac \)[/tex]:
[tex]\[
4ac = 4 \times 1 \times (-3) = -12
\][/tex]
3. Substitute the calculated values into the discriminant formula:
[tex]\[
D = 81 - (-12) = 81 + 12 = 93
\][/tex]
Therefore, the discriminant of the quadratic equation [tex]\(x^2 - 9x - 3 = 0\)[/tex] is 93.
