Function f is defined as f(x) = x^2 + 17x + 60. What is the solution set for f(x) = 0?
A.) {5,12}
B.) { - 12, - 5}
C.) { - 3, 20}
D.) { - 20, 3}
To find the solution set for f(x) = 0, we need to solve the quadratic equation x^2 + 17x + 60 = 0. We can do this by factoring or by using the quadratic formula.
By factoring, we look for two numbers that multiply to give 60 and add to give 17. The numbers are 5 and 12. So, the factored form of the equation is (x + 5)(x + 12) = 0. To solve for x, we set each factor equal to zero:
x + 5 = 0
x = -5
x + 12 = 0
x = -12
Therefore, the solution set for f(x) = 0 is {-5, -12}.
The correct answer is B.) { - 12, - 5}