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use the given zereo to find the remaining zereos of the function.

Use The Given Zereo To Find The Remaining Zereos Of The Function class=

Sagot :

Given the function:

[tex]f(x)=x^3-5x^2+36x-180[/tex]

The given function has 3 zeros

one of the zeros = -6i

so, the second one will be a conjugate to the first zero

So, the second one = 6i

The product of the three zeros = -180

let the third zero = a

So,

[tex]\begin{gathered} -6i\cdot6i\cdot b=-180 \\ -36i^2\cdot b=180 \\ -36\cdot-1\cdot b=180 \\ 36b=180 \\ \\ b=\frac{180}{35}=5 \end{gathered}[/tex]

So, the third zero = 5

So, the answer will be:

The remaining zeros of the function are: 6i and 5

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