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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 2 x^{3} - 2 x - 1$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

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

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

The polynomial generated from the given zeros is: P(x)=x4+2x3−2x−1

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

The polynomial generated from the given zeros is: $P (x) = x^{4} + 2 x^{3} - 2 x - 1$