The roots of the quadratic equation z^2 + az + b = 0 are 2 - 3i and 2 + 3i. What is a + b?
(z-2+3i)(z-2-3i) = 0 now multiply
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To find the sum of the roots of a quadratic equation, we can use the fact that the sum of the roots is equal to the negation of the coefficient of the linear term (a) divided by the coefficient of the quadratic term (1).
Given that the roots of the quadratic equation are 2 - 3i and 2 + 3i, we know they add up to give us 4.
So, the sum of the roots, 4, is equal to -a/1.
Therefore, -a = 4, and solving for a gives us a = -4.
To find b, we can use the fact that the product of the roots is equal to the constant term (b) divided by the coefficient of the quadratic term (1).
The product of the roots is (2 - 3i)(2 + 3i), which simplifies to 4 - (3i)^2, or 4 - 9i^2. Since i^2 is equal to -1, the expression becomes 4 + 9, or 13.
Therefore, the product of the roots, 13, is equal to b/1.
Therefore, b = 13.
To find a + b, we can sum up the values of a and b that we found earlier:
a + b = -4 + 13 = 9.
So, a + b is equal to 9.