In the equation x² + mx + n = 0, m and n are integers. The only possible value for x is -3. What is the value of m?

A.) 3

B.) -3

C.) 6

D.) -6

E.) 9

A.) 3

B.) -3

C.) 6

D.) -6

E.) 9

If the only possible value for x is -3, and it is a parabola, then the parabola would be touching the x-axis at -3, such as in the graph below:

If x = -3, and it is a parabola, then the solution would be -3 with a multiplicity of 2.

Work backwards from the solution:

x = -3 or x = -3 {set x = -3, twice, since the multiplicity of -3 is 2}

x + 3 = 0 or x + 3 = 0 {added 3 to each side}

(x +3)(x + 3) = 0 {multiplied and set equal to 0}

x² + 6x + 9 = 0 {used foil method}

Work backwards from the solution:

x = -3 or x = -3 {set x = -3, twice, since the multiplicity of -3 is 2}

x + 3 = 0 or x + 3 = 0 {added 3 to each side}

(x +3)(x + 3) = 0 {multiplied and set equal to 0}

x² + 6x + 9 = 0 {used foil method}

**The value of m is 6.****C.)***- Algebra House*