Question

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tutorial exercise
use the given zero to find all the zeros of the function. (enter your answers as a comma - separated list. include the given zero in your answer.)
function: (f(x)=x^{3}+x^{2}+49x + 49) zero: (7i)
step 1
since the polynomial has real coefficients, the complex conjugate is also a zero of the function. therefore, since (7i) is a zero, (\boldsymbol{quad}) is also a zero of the function.
enter a mathematical expression.
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Explanation:

Step1: Apply Complex Conjugate Root Theorem

For polynomials with real coefficients, if \(a+bi\) is a zero, then \(a-bi\) is also a zero. Given zero is \(7i = 0+7i\), so its conjugate is \(0-7i=-7i\).

Answer:

\(-7i\)