Answer :
We are given the quadratic equation
[tex]$$
9x^2 + x + 5 = 0.
$$[/tex]
The first step is to identify the coefficients from the general form of a quadratic equation, which is
[tex]$$
ax^2 + bx + c = 0.
$$[/tex]
Here, the coefficients are:
- [tex]$a = 9$[/tex]
- [tex]$b = 1$[/tex]
- [tex]$c = 5$[/tex]
The discriminant of a quadratic equation is given by
[tex]$$
\Delta = b^2 - 4ac.
$$[/tex]
Now, we compute each part step by step:
1. Compute [tex]$b^2$[/tex]:
[tex]$$
b^2 = 1^2 = 1.
$$[/tex]
2. Compute [tex]$4ac$[/tex]:
[tex]$$
4ac = 4 \times 9 \times 5 = 180.
$$[/tex]
3. Now, substitute these into the discriminant formula:
[tex]$$
\Delta = b^2 - 4ac = 1 - 180 = -179.
$$[/tex]
So, the discriminant of the quadratic equation is
[tex]$$
\boxed{-179}.
$$[/tex]
This is the final result.
[tex]$$
9x^2 + x + 5 = 0.
$$[/tex]
The first step is to identify the coefficients from the general form of a quadratic equation, which is
[tex]$$
ax^2 + bx + c = 0.
$$[/tex]
Here, the coefficients are:
- [tex]$a = 9$[/tex]
- [tex]$b = 1$[/tex]
- [tex]$c = 5$[/tex]
The discriminant of a quadratic equation is given by
[tex]$$
\Delta = b^2 - 4ac.
$$[/tex]
Now, we compute each part step by step:
1. Compute [tex]$b^2$[/tex]:
[tex]$$
b^2 = 1^2 = 1.
$$[/tex]
2. Compute [tex]$4ac$[/tex]:
[tex]$$
4ac = 4 \times 9 \times 5 = 180.
$$[/tex]
3. Now, substitute these into the discriminant formula:
[tex]$$
\Delta = b^2 - 4ac = 1 - 180 = -179.
$$[/tex]
So, the discriminant of the quadratic equation is
[tex]$$
\boxed{-179}.
$$[/tex]
This is the final result.
