Question

solve ( x^2 - 4x + 3 = 0 ) using the quadratic formula.

( x = square ) and ( x = square )

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
For the equation \(x^2 - 4x + 3 = 0\), we have \(a = 1\), \(b=-4\), and \(c = 3\).

Step2: Calculate the Discriminant

First, calculate the discriminant \(D=b^2 - 4ac\).
Substitute \(a = 1\), \(b=-4\), \(c = 3\) into the discriminant formula:
\(D=(-4)^2-4\times1\times3\)
\(=16 - 12\)
\(= 4\)

Step3: Apply Quadratic Formula

Now, substitute \(a = 1\), \(b=-4\), and \(D = 4\) into the quadratic formula:
\(x=\frac{-(-4)\pm\sqrt{4}}{2\times1}\)
\(=\frac{4\pm2}{2}\)

Step4: Find the Two Solutions

For the plus sign:
\(x=\frac{4 + 2}{2}=\frac{6}{2}=3\)
For the minus sign:
\(x=\frac{4-2}{2}=\frac{2}{2}=1\)

Answer:

\(x = 1\) and \(x = 3\)