Question

If f(x) = 20 - 7x^2 + 7x + 15 and f(3) = 0, then find all of the zeros of f(x) algebraically.

a) x = -3, x = 1
b) x = -1, x = 3
c) x = -2, x = 4
d) x = 0, x = 5

Answer 1

To find the zeros of the given function algebraically, one must correct the polynomial to its standard quadratic form and then apply the quadratic formula or factor the quadratic polynomial, after accounting for the known zero, x = 3.

Step-by-step explanation:

The question asks us to find all the zeros of the function f(x) = 20 - 7x^2 + 7x + 15 algebraically, given that f(3) = 0. From the given information, we know that x = 3 is a root of the equation. To find the other roots of the polynomial, we can divide the polynomial by (x - 3) or use the quadratic formula to find the other zero(s). The correct coefficient of x^2 should be given by the standard quadratic form ax^2 + bx + c, so the polynomial when correctly expressed would be -7x^2 + 7x + 35 after combining like terms from the original function.

We can further simplify the equation to find the other roots. Since f(3) = 0 and f(x) is a quadratic function, the other root must satisfy the equation after we factor it. However, since the coefficients in the polynomial are not correct as given, assuming a transcription error for the original function, we will instead correct the coefficients and proceed with the factoring method or the quadratic formula to find the remaining zero(s).

Answer 2

There are no zeros for the given function.

Step-by-step explanation:

To find the zeros of the function f(x) = 20 - 7x^2 + 7x + 15 algebraically, we set f(x) = 0 and solve for x.

Substituting x = 3 into the function, we get:

0 = 20 - 7(3)^2 + 7(3) + 15

Simplifying, we have:

0 = 20 - 63 + 21 + 15

0 = -7

Since this gives us an inconsistent equation, there are no zeros for the function f(x).