Find the solution set for x.
x^2 + 8x + 15 = 0
a) (2,4)
b) (3,5)
c) (-2,-4)
d) (-3,-5)
What numbers will give a product of 15 and a sum of 8?
x=2 and x=5
To find the solution set for the equation x^2 + 8x + 15 = 0, we can use the quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 8, and c = 15.
Plugging in these values into the quadratic formula, we get:
x = (-8 ± √(8^2 - 4(1)(15))) / (2(1))
Simplifying further:
x = (-8 ± √(64 - 60)) / 2
x = (-8 ± √4) / 2
x = (-8 ± 2) / 2
This gives us two possible solutions:
x = (-8 + 2) / 2 = -6 / 2 = -3
x = (-8 - 2) / 2 = -10 / 2 = -5
Therefore, the solution set for x is { -3, -5 }. So, the correct option is d) (-3, -5).