The quadratic equation x2 + mx + q = 0, where m and q are real numbers, has the complex root a + bi. Which of the following must be equal to m?

Which of what following?

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And what do you think is the right one?

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To solve this problem, we need to understand the relationship between the coefficients of a quadratic equation and its roots.

The given quadratic equation is x^2 + mx + q = 0, and it has a complex root a + bi.

For a quadratic equation with real coefficients to have a complex root, the conjugate of that complex root must also be a root. So, the complex root a + bi implies that the conjugate a - bi must also be a root of the equation.

We know that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of x (m) divided by the coefficient of x^2 (which is always 1).

Therefore, the sum of the roots is (a + bi) + (a - bi) = 2a. So, 2a = -m.

From this equation, we can conclude that m must be equal to -2a.

Therefore, m = -2a.

Now, we need to determine which of the given options satisfy m = -2a.

Without the given options, we cannot determine the specific value of m. However, we can conclude that m is some multiple of -2a.

So, none of the options given will always be equal to m.