Find the polynomial having roots at $- 5$ , $0$ , $3$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 5 x^{3} - 9 x^{2} - 45 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 5$	$x + 5$
$0$	$x$
$3$	$x - 3$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

P (x) = (x + 5) \cdot x \cdot (x - 3) \cdot (x + 3) = x^{4} + 5 x^{3} - 9 x^{2} - 45 x

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Find the polynomial having roots at −5 , 0 , 3 and −3 .

The polynomial generated from the given zeros is: P(x)=x4+5x3−9x2−45x

Find the polynomial having roots at $- 5$ , $0$ , $3$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} + 5 x^{3} - 9 x^{2} - 45 x$