Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is [tex]\( x = \frac{-3 \pm \sqrt{3^2 - 4(1)(2)}}{2(1)} \)[/tex] after substituting the values of [tex]\( a, b \)[/tex], and [tex]\( c \)[/tex] into the formula. Which is Ramiya's quadratic equation?

Quadratic formula: [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex]

A. [tex]\( 0 = x^2 + 3x + 2 \)[/tex]
B. [tex]\( 0 = x^2 - 3x + 2 \)[/tex]
C. [tex]\( 0 = 2x^2 + 3x + 1 \)[/tex]
D. [tex]\( 0 = 2x^2 - 3x + 1 \)[/tex]



Answer :

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