Find the polynomial having roots at $0$ , $- 1$ , $- 1$ and $2$ .

Answer

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

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$- 1$	$x + 1$
$- 1$	$x + 1$
$2$	$x - 2$

Step 2: Multiply the factors together:

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

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Find the polynomial having roots at 0 , −1 , −1 and 2 .

The polynomial generated from the given zeros is: P(x)=x4−3x2−2x

Find the polynomial having roots at $0$ , $- 1$ , $- 1$ and $2$ .

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