Find the polynomial having roots at $0$ , $2$ , $8$ and $- 2$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 8 x^{3} - 4 x^{2} + 32 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$2$	$x - 2$
$8$	$x - 8$
$- 2$	$x + 2$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 2) \cdot (x - 8) \cdot (x + 2) = x^{4} - 8 x^{3} - 4 x^{2} + 32 x

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Find the polynomial having roots at 0 , 2 , 8 and −2 .

The polynomial generated from the given zeros is: P(x)=x4−8x3−4x2+32x

Find the polynomial having roots at $0$ , $2$ , $8$ and $- 2$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 8 x^{3} - 4 x^{2} + 32 x$