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Given the polynomial f(x) = x2 + px + 12 and one of its zeros is x=4.

May 10, 2026Mathematics

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Answer

\text{-7}

3 steps

Understand the definition of a zero of a polynomial.
If $x=a$ is a zero of a polynomial $f(x)$ , it means that when $x=a$ is substituted into the polynomial, the result is 0, i.e., $f(a) = 0$ .
Substitute the given zero into the polynomial.
Given the polynomial $f(x) = x^2 + px + 12$ and one of its zeros is $x=4$ .
Therefore, we set $f(4) = 0$ .
Set up the equation and solve for $p$ .
Substitute $x=4$ into the polynomial:
$(4)^2 + p(4) + 12 = 0$ $16 + 4p + 12 = 0$ $4p + 28 = 0$
Subtract 28 from both sides:
$4p = -28$
Divide by 4:
$p = \frac{-28}{4}$ $p = -7$
The value of the constant $p$ is $\boxed{\text{-7}}$ .

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