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