Question

1. $x^{2}+4x + 3 = 0$

a = \underline{\quad} b = \underline{\quad} c = \underline{\quad}
substitute into the quadratic formula:

what are the x - intercepts?
\underline{\quad},\underline{\quad}

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), in \(x^2 + 4x + 3 = 0\), \(a = 1\), \(b = 4\), \(c = 3\).

Step2: Quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute \(a = 1\), \(b = 4\), \(c = 3\):
\(x=\frac{-4\pm\sqrt{4^2 - 4\times1\times3}}{2\times1}=\frac{-4\pm\sqrt{16 - 12}}{2}=\frac{-4\pm\sqrt{4}}{2}=\frac{-4\pm2}{2}\)

Step3: Solve for x

Case 1: \(x=\frac{-4 + 2}{2}=\frac{-2}{2}=-1\)
Case 2: \(x=\frac{-4 - 2}{2}=\frac{-6}{2}=-3\)

Answer:

\(a = 1\), \(b = 4\), \(c = 3\); \(x\)-intercepts: \(-1\), \(-3\)