Find the zeros of the function algebraically. (Enter your answers as a comma-separated list.)
f(x) = 2x2 − 3x − 20
x =
(2x + 5)(x - 4) = 2 x^2 + 5 x - 8 x - 20
= 2 x^2 -3 x -20
so
4 and -5/2
Sure, here's your answer: The zeros of the function f(x) = 2x^2 - 3x - 20 are x = -2.5 and x = 4.
To find the zeros of the function algebraically, we need to find the values of x for which f(x) equals zero. In other words, we need to solve the equation 2x^2 - 3x - 20 = 0.
Let's use the quadratic formula to solve this equation:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 2, b = -3, and c = -20.
x = (-(-3) ± √((-3)^2 - 4(2)(-20))) / 2(2)
= (3 ± √(9 + 160)) / 4
= (3 ± √169) / 4
= (3 ± 13) / 4
We have two possible solutions:
x1 = (3 + 13) / 4 = 16 / 4 = 4
x2 = (3 - 13) / 4 = -10 / 4 = -2.5
Therefore, the zeros of the function f(x) = 2x^2 - 3x - 20 algebraically are x = 4 and x = -2.5.
To find the zeros of the function algebraically, we need to solve the equation f(x) = 0. In this case, the equation is:
2x^2 - 3x - 20 = 0
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = -3, and c = -20. Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(2)(-20))) / (2(2))
Simplifying the formula:
x = (3 ± √(9 + 160)) / 4
x = (3 ± √169) / 4
Now, let's simplify further:
x = (3 ± 13) / 4
We have two possible solutions:
x = (3 + 13) / 4 = 16 / 4 = 4
or
x = (3 - 13) / 4 = -10 / 4 = -5/2
Therefore, the zeros of the function f(x) = 2x^2 - 3x - 20 are x = 4 and x = -5/2.