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

f(x) = 3x2 + 5x + 4

f(x) = 3x2 + 15x + 12

f(x) = 3x2 – 5x + 4

f(x) = 3x2 – 15x + 12

Verified Answer :

jameeovaljameerocks

It's D I took the test

carlosego

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:

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

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