Question

An equation is shown. x2+4x+3=0 . Complete the statements. Desmos Calculator (click here) (4 points) The value of a is 1 . The value of b is 4 . The value of c is 3. write a quadratic equation, and find a soloution.

Answer 1

You're given the quadratic equation \(x^2 + 4x + 3 = 0\).

You correctly identified:
- The value of \(a\) is 1 (coefficient of \(x^2\)).
- The value of \(b\) is 4 (coefficient of \(x\)).
- The value of \(c\) is 3 (constant term).

Now, let's rewrite the quadratic equation in the standard form:

\[
1x^2 + 4x + 3 = 0
\]

### Finding the Solutions

To find the solutions of the quadratic equation, you can use the quadratic formula:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]

Substituting in the values of \(a\), \(b\), and \(c\):

\[
x = \frac{{-4 \pm \sqrt{{4^2 - 4 \cdot 1 \cdot 3}}}}{2 \cdot 1}
\]
\[
x = \frac{{-4 \pm \sqrt{{16 - 12}}}}{2}
\]
\[
x = \frac{{-4 \pm \sqrt{4}}}{2}
\]
\[
x = \frac{{-4 \pm 2}}{2}
\]

This results in two possible solutions:

1. \(x = \frac{{-4 + 2}}{2} = \frac{{-2}}{2} = -1\)

2. \(x = \frac{{-4 - 2}}{2} = \frac{{-6}}{2} = -3\)

### Summary of the Solutions

The solutions to the equation \(x^2 + 4x + 3 = 0\) are:
- \(x = -1\)
- \(x = -3\)

These are the roots of the quadratic equation.