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write a polynomial function in standard form with real coefficients whose zeros include 2, 5 i and -5 icheck the photo for more info pls!

write a polynomial function in standard form with real coefficients whose zeros include 2, 5 i and -5 icheck the photo for more info pls! class=

Answer :

Given

The zeros are given 2, 5 i and -5 i.

Explanation

To determine the polynomial function ,

Use the general expression for the polynomial.

[tex](x-a)(x-b)(x-c)=0[/tex]

Substitute the values,

[tex](x-2)(x-5i)(x+5i)=0[/tex]

Use the identity to simplify the expression

[tex](a-b)(a+b)=a^2-b^2[/tex]

Then the expression becomes.

[tex]\begin{gathered} (x-2)(x^2-(5i)^2)=(x-2)(x^2+25) \\ (x-2)(x^2+25)=x^3+25x-2x^2-50 \end{gathered}[/tex]

Answer

The answer is

[tex]f(x)=x^3-2x^2+25x-50[/tex]

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