Question

solve for p.
\\( p^2 - 23p + 22 = 0 \\)
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
\\( p = \\)

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(22\) and add up to \(-23\). The numbers are \(-1\) and \(-22\) because \((-1)\times(-22) = 22\) and \((-1)+(-22)=-23\). So we can factor the quadratic as:
\(p^{2}-23p + 22=(p - 1)(p - 22)=0\)

Step2: Solve for p

Set each factor equal to zero:
For \(p - 1=0\), we get \(p = 1\).
For \(p - 22=0\), we get \(p = 22\).

Answer:

\(1,22\)