Question

solve for v.

$v^2 - v - 2 = 0$

if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Factor the quadratic equation

We have the quadratic equation \(v^2 - v - 2 = 0\). We need to find two numbers that multiply to \(-2\) and add up to \(-1\). The numbers are \(-2\) and \(1\) since \((-2)\times1=-2\) and \(-2 + 1=-1\). So we can factor the equation as \((v - 2)(v+ 1)=0\)

Step2: Solve for \(v\) using zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For \((v - 2)(v + 1)=0\), we set each factor equal to zero:

• If \(v-2=0\), then by adding \(2\) to both sides of the equation, we get \(v = 2\).
• If \(v + 1=0\), then by subtracting \(1\) from both sides of the equation, we get \(v=-1\).

Answer:

\(2,-1\)