Question

identify the solution(s) of ( m^2 + 3m + 2 = 0 )
no solution (quad m = -9 quad m = -8 quad m = -7 quad m = -6 )
( m = -5 quad m = -4 quad m = -3 quad m = -2 quad m = -1 )
( m = 0 quad m = 1 quad m = 2 quad m = 3 quad m = 4 )
( m = 5 quad m = 6 quad m = 7 quad m = 8 quad m = 9 )

Explanation:

Step1: Factor the quadratic equation

We factor \( m^2 + 3m + 2 = 0 \). We need two numbers that multiply to \( 2 \) and add to \( 3 \). The numbers are \( 1 \) and \( 2 \). So, \( m^2 + 3m + 2=(m + 1)(m+ 2)=0 \).

Step2: Solve for \( m \)

Using the zero - product property, if \( (m + 1)(m + 2)=0 \), then either \( m+1 = 0 \) or \( m + 2=0 \).

• If \( m+1=0 \), then \( m=-1 \).
• If \( m + 2=0 \), then \( m=-2 \).

Answer:

\( m=-1 \), \( m = - 2 \) (from the given options, \( m=-2 \) and \( m=-1 \) are the solutions)