Answer :
We are given the quadratic equation
[tex]$$
-9x^2 - x - 5 = 0.
$$[/tex]
Step 1. Identify the coefficients
The standard form of a quadratic equation is
[tex]$$
ax^2 + bx + c = 0.
$$[/tex]
Comparing, we have:
[tex]$$
a = -9,\quad b = -1,\quad c = -5.
$$[/tex]
Step 2. Write the formula for the discriminant
The discriminant [tex]\( D \)[/tex] is given by:
[tex]$$
D = b^2 - 4ac.
$$[/tex]
Step 3. Calculate [tex]\( b^2 \)[/tex]
Substitute [tex]\( b = -1 \)[/tex]:
[tex]$$
b^2 = (-1)^2 = 1.
$$[/tex]
Step 4. Calculate [tex]\( 4ac \)[/tex]
Substitute [tex]\( a = -9 \)[/tex] and [tex]\( c = -5 \)[/tex]:
[tex]$$
4ac = 4 \times (-9) \times (-5) = 180.
$$[/tex]
Step 5. Compute the discriminant
Substitute the calculated values into the formula:
[tex]$$
D = 1 - 180 = -179.
$$[/tex]
Thus, the discriminant of the quadratic equation is
[tex]$$
-179.
$$[/tex]
[tex]$$
-9x^2 - x - 5 = 0.
$$[/tex]
Step 1. Identify the coefficients
The standard form of a quadratic equation is
[tex]$$
ax^2 + bx + c = 0.
$$[/tex]
Comparing, we have:
[tex]$$
a = -9,\quad b = -1,\quad c = -5.
$$[/tex]
Step 2. Write the formula for the discriminant
The discriminant [tex]\( D \)[/tex] is given by:
[tex]$$
D = b^2 - 4ac.
$$[/tex]
Step 3. Calculate [tex]\( b^2 \)[/tex]
Substitute [tex]\( b = -1 \)[/tex]:
[tex]$$
b^2 = (-1)^2 = 1.
$$[/tex]
Step 4. Calculate [tex]\( 4ac \)[/tex]
Substitute [tex]\( a = -9 \)[/tex] and [tex]\( c = -5 \)[/tex]:
[tex]$$
4ac = 4 \times (-9) \times (-5) = 180.
$$[/tex]
Step 5. Compute the discriminant
Substitute the calculated values into the formula:
[tex]$$
D = 1 - 180 = -179.
$$[/tex]
Thus, the discriminant of the quadratic equation is
[tex]$$
-179.
$$[/tex]
