Answer :
To find the discriminant of the quadratic equation [tex]\(-9x^2 - x - 5 = 0\)[/tex], we'll use the discriminant formula. The discriminant [tex]\( D \)[/tex] of a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] is given by:
[tex]\[ D = b^2 - 4ac \][/tex]
Let's identify the coefficients from the equation:
- [tex]\( a = -9 \)[/tex]
- [tex]\( b = -1 \)[/tex]
- [tex]\( c = -5 \)[/tex]
Now, we can substitute these values into the discriminant formula:
[tex]\[ D = (-1)^2 - 4(-9)(-5) \][/tex]
Now calculate each part:
1. [tex]\((-1)^2 = 1\)[/tex]
2. Calculate [tex]\(4 \times (-9) \times (-5)\)[/tex]:
[tex]\[ 4 \times 9 \times 5 = 180 \][/tex]
Now substitute back:
[tex]\[ D = 1 - 180 \][/tex]
Finally, perform the subtraction:
[tex]\[ D = 1 - 180 = -179 \][/tex]
So, the discriminant of the quadratic equation [tex]\(-9x^2 - x - 5 = 0\)[/tex] is [tex]\(-179\)[/tex].
[tex]\[ D = b^2 - 4ac \][/tex]
Let's identify the coefficients from the equation:
- [tex]\( a = -9 \)[/tex]
- [tex]\( b = -1 \)[/tex]
- [tex]\( c = -5 \)[/tex]
Now, we can substitute these values into the discriminant formula:
[tex]\[ D = (-1)^2 - 4(-9)(-5) \][/tex]
Now calculate each part:
1. [tex]\((-1)^2 = 1\)[/tex]
2. Calculate [tex]\(4 \times (-9) \times (-5)\)[/tex]:
[tex]\[ 4 \times 9 \times 5 = 180 \][/tex]
Now substitute back:
[tex]\[ D = 1 - 180 \][/tex]
Finally, perform the subtraction:
[tex]\[ D = 1 - 180 = -179 \][/tex]
So, the discriminant of the quadratic equation [tex]\(-9x^2 - x - 5 = 0\)[/tex] is [tex]\(-179\)[/tex].
