Find the polynomial having roots at $- 9$ , $1$ , $0$ , $1$ and $9$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - 2 x^{4} - 80 x^{3} + 162 x^{2} - 81 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 9$	$x + 9$
$1$	$x - 1$
$0$	$x$
$1$	$x - 1$
$9$	$x - 9$

Step 2: Multiply the factors together:

P (x) = (x + 9) \cdot (x - 1) \cdot x \cdot (x - 1) \cdot (x - 9) = x^{5} - 2 x^{4} - 80 x^{3} + 162 x^{2} - 81 x

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Find the polynomial having roots at −9 , 1 , 0 , 1 and 9 .

The polynomial generated from the given zeros is: P(x)=x5−2x4−80x3+162x2−81x

Find the polynomial having roots at $- 9$ , $1$ , $0$ , $1$ and $9$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - 2 x^{4} - 80 x^{3} + 162 x^{2} - 81 x$