To determine Ramiya's quadratic equation from the given options, we need to analyze the quadratic equation she is trying to solve using the quadratic formula.
The quadratic formula is given by:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
We are provided with Ramiya's version of this formula:
[tex]\[
x = \frac{-3 \pm \sqrt{3^2 - 4(1)(2)}}{2(1)}
\][/tex]
From her formula, we can see:
- The coefficient [tex]\(a = 1\)[/tex]
- The coefficient [tex]\(b = 3\)[/tex]
- The constant term [tex]\(c = 2\)[/tex]
Using these values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], we can rewrite the standard form of the quadratic equation, which is:
[tex]\[
0 = a x^2 + b x + c
\][/tex]
Substituting [tex]\(a = 1\)[/tex], [tex]\(b = 3\)[/tex], and [tex]\(c = 2\)[/tex] into this form, we get:
[tex]\[
0 = 1 x^2 + 3 x + 2
\][/tex]
or simply:
[tex]\[
0 = x^2 + 3 x + 2
\][/tex]
Therefore, the correct quadratic equation that Ramiya is solving is:
[tex]\[
0 = x^2 + 3 x + 2
\][/tex]
So, the correct choice from the given options is:
0 = x^2 + 3x + 2
