Question

k² - 8k + 7 = 0
show your work here
k =
k =

Explanation:

Step1: Factor the quadratic equation

We have the quadratic equation \(k^{2}-8k + 7=0\). We need to find two numbers that multiply to \(7\) and add up to \(- 8\). The numbers are \(-1\) and \(-7\) since \((-1)\times(-7)=7\) and \((-1)+(-7)=-8\). So we can factor the equation as \((k - 1)(k - 7)=0\)

Step2: Solve for k

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So from \((k - 1)(k - 7)=0\), we have two cases:
Case 1: \(k-1=0\), then \(k = 1\)
Case 2: \(k - 7=0\), then \(k=7\)

Answer:

\(k = 1\) and \(k = 7\)