Find the polynomial having roots at $1$ , $- 1$ , $3$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 10 x^{2} + 9$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$- 1$	$x + 1$
$3$	$x - 3$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x + 1) \cdot (x - 3) \cdot (x + 3) = x^{4} - 10 x^{2} + 9

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Find the polynomial having roots at 1 , −1 , 3 and −3 .

The polynomial generated from the given zeros is: P(x)=x4−10x2+9

Find the polynomial having roots at $1$ , $- 1$ , $3$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 10 x^{2} + 9$