I really need help with this question. Thanks! Find the zeros of the function algebraically. Be sure to show all work.
f(x)=x^2-8x+15
---------------
10x
First factor x^2-8x+15
You should get
(x-5)(x-3)
Now set each factor equal to zero and solve for x
x-5=0
x-3=0
@Mia, did I do this write?
x^2-8x+15
(x + 3) (x + 5)
x-5=0 x-3=0
The zeros would be x = 3 x = 5
Yes
To find the zeros of the function f(x) algebraically, we need to solve the equation f(x) = 0.
The given function is:
f(x) = x^2 - 8x + 15
_______
10x
To simplify the equation, let's multiply both sides of the equation by 10x to eliminate the denominator:
10x * f(x) = 10x * (x^2 - 8x + 15)
This gives us:
10x^2 - 80x + 150 = 0
Now, we have a quadratic equation in standard form (ax^2 + bx + c = 0), where a = 10, b = -80, and c = 150. To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula.
Let's try factoring:
10x^2 - 80x + 150 = 0
Divide each term by the common factor of 10:
x^2 - 8x + 15 = 0
Now, we need to find two numbers that multiply to give 15 and add up to -8 (the coefficient of x).
The two numbers are -3 and -5:
(x - 3)(x - 5) = 0
Now, we have factored the quadratic equation. To find the zeros, we set each factor equal to zero and solve for x:
x - 3 = 0 or x - 5 = 0
Solving each equation, we get:
x = 3 or x = 5
Therefore, the zeros of the function f(x) = x^2 - 8x + 15 / 10x are x = 3 and x = 5.