Question

In the equation x^2 + mx + n = 0, m and m are integers. The only possible value for x is -3. What is the value of m?

Answer 1

If there is only one solution, at x=-3, then the factor of (x+3) must be repeated. The equation must be equivalent to

... (x +3)² = 0

This multiplies out to give

... x² +6x +9 = 0

The value of m is 6.

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For finding the square of a binomial, you can either use the special form you have memorized:

... (x +a)² + x² +2ax + a²

or you can use the distributive property.

... (x +a)² = x(x +a) +a(x +a)

... = x² +ax +ax +a² = x² +2ax +a²