How do I solve this step by step?
What are the roots of f(x)=x^2+2x−8f(x)=x2+2x−8?
assume you mean y =x^2+2x−8
where is y = 0?
y = (x+4)(x-2) = 0
x= 2 works and x = -4 works
To find the roots of the equation f(x) = x^2 + 2x - 8, you can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = -8. Plugging these values into the quadratic formula, we get:
x = (-(2) ± √((2)^2 - 4(1)(-8))) / (2(1))
Simplifying further:
x = (-2 ± √(4 + 32)) / 2
x = (-2 ± √36) / 2
x = (-2 ± 6) / 2
Now we have two possibilities:
1. x = (-2 + 6) / 2 = 4 / 2 = 2
2. x = (-2 - 6) / 2 = -8 / 2 = -4
Therefore, the roots of the equation f(x) = x^2 + 2x - 8 are x = 2 and x = -4.