Question

blake knows that one of the solutions to (x^2 - 6x + 8 = 0) is (x = 2). what is the other solution?
( \bigcirc x = -6 )
( \bigcirc x = -3 )
( \bigcirc x = 4 )
( \bigcirc x = 8 )

Explanation:

Step1: Recall Vieta's Formula

For a quadratic equation \(ax^2 + bx + c = 0\), the sum of the roots \(r_1\) and \(r_2\) is \(-\frac{b}{a}\).
Here, the equation is \(x^2 - 6x + 8 = 0\), so \(a = 1\), \(b = -6\), \(c = 8\). Let one root \(r_1 = 2\) and the other root be \(r_2\).

Step2: Apply Vieta's Formula

The sum of the roots \(r_1 + r_2 = -\frac{b}{a}\). Substituting the values, we get \(2 + r_2 = -\frac{-6}{1}= 6\).

Step3: Solve for \(r_2\)

Subtract 2 from both sides: \(r_2 = 6 - 2 = 4\).

Answer:

\(x = 4\) (corresponding to the option "x = 4")