The polynomial that has the zeros when x = 5, 1/3 and -7 is [tex]P(x) = (x - 5) (x - \frac 13) (x + 7)[/tex]
The zeros of the polynomial are given as:
Rewrite the above equations, as follows:
Multiply the above equations
[tex](x - 5) \times (x - \frac 13) \times (x + 7) = 0 \times 0 \times 0[/tex]
[tex](x - 5) \times (x - \frac 13) \times (x + 7) = 0[/tex]
Remove the product sign
[tex](x - 5) (x - \frac 13) (x + 7) = 0[/tex]
Rewrite the above as a function
[tex]P(x) = (x - 5) (x - \frac 13) (x + 7)[/tex]
Hence, the polynomial that has the zeros when x = 5, 1/3 and -7 is [tex]P(x) = (x - 5) (x - \frac 13) (x + 7)[/tex]
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