Find the polynomial having roots at $- 3$ , $- 2$ , $2$ , $4$ and $0$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - x^{4} - 16 x^{3} + 4 x^{2} + 48 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 3$	$x + 3$
$- 2$	$x + 2$
$2$	$x - 2$
$4$	$x - 4$
$0$	$x$

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x + 2) \cdot (x - 2) \cdot (x - 4) \cdot x = x^{5} - x^{4} - 16 x^{3} + 4 x^{2} + 48 x

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Find the polynomial having roots at −3 , −2 , 2 , 4 and 0 .

The polynomial generated from the given zeros is: P(x)=x5−x4−16x3+4x2+48x

Find the polynomial having roots at $- 3$ , $- 2$ , $2$ , $4$ and $0$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - x^{4} - 16 x^{3} + 4 x^{2} + 48 x$