Question

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

Answer 1

It's D I took the test

Answer 2

For this case we have that the following function complies with the given conditions:

$f (x) = 3x ^ 2 - 15x + 12$

To prove it, let's find the roots of the polynomial:

$3x ^ 2 - 15x + 12 = 0$

By doing common factor 3 we have:

$3 (x ^ 2 - 5x + 4) = 0$

Factoring the second degree polynomial we have:

$3 (x-1) (x-4) = 0$

Then, the solutions are:

Solution 1:

$x-1 = 0\\x = 1$

Solution 2:

$x-4 = 0\\x = 4$

Answer:

A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:

$f (x) = 3x ^ 2 - 15x + 12$