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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 6 x^{2} + 8 x$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = x \cdot (x + 2) \cdot (x + 4) = x^{3} + 6 x^{2} + 8 x

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

The polynomial generated from the given zeros is: P(x)=x3+6x2+8x

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

The polynomial generated from the given zeros is: $P (x) = x^{3} + 6 x^{2} + 8 x$