Find the polynomial having roots at $- 2$ , $2$ , $- 3$ , $3$ , $4$ and $- 4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{6} - 29 x^{4} + 244 x^{2} - 576$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 2$	$x + 2$
$2$	$x - 2$
$- 3$	$x + 3$
$3$	$x - 3$
$4$	$x - 4$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = (x + 2) \cdot (x - 2) \cdot (x + 3) \cdot (x - 3) \cdot (x - 4) \cdot (x + 4) = x^{6} - 29 x^{4} + 244 x^{2} - 576

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Find the polynomial having roots at −2 , 2 , −3 , 3 , 4 and −4 .

The polynomial generated from the given zeros is: P(x)=x6−29x4+244x2−576

Find the polynomial having roots at $- 2$ , $2$ , $- 3$ , $3$ , $4$ and $- 4$ .

The polynomial generated from the given zeros is: $P (x) = x^{6} - 29 x^{4} + 244 x^{2} - 576$