Answered

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you were given the polynomial f(x)=3x^3+13x^2+19x+k and you know that f(-2)=0find k

Sagot :

Answer:

k = 10

Explanation:

The initial polynomial is:

[tex]f(x)=3x^3+13x^2+19x+k[/tex]

If f(-2) = 0, then when we replace x by -2, the result will be 0. It means that we can write the following equation:

[tex]\begin{gathered} f(-2)=3(-2)^3+13(-2)^2+19(-2)+k=0 \\ 3(-2)^3+13(-2)^2+19(-2)+k=0 \end{gathered}[/tex]

Therefore, we can solve for k as follows:

[tex]\begin{gathered} 3(-8)+13(4)+19(-2)+k=0 \\ -24+52-38+k=0 \\ -10+k=0 \\ -10+k+10=0+10 \\ k=10 \end{gathered}[/tex]

So, the value of k is 10

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