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If m  is a real number and $$x^2 + mx + m$$ has two distinct real roots, then what are the possible values of m? Express your answer in interval notation.

May 17, 2022

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The quadratic polynomial has two distinct real roots. That means the discriminant must be positive.

$$\Delta > 0\\ m^2 - 4(1)(m) > 0\\ m^2 - 4m > 0\\ m > 4\text{ or }m < 0$$

Can you write that inequality in interval notation?

May 18, 2022