Find the polynomial having roots at $- 1$ , $2$ and $- 4$ .

Answer

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

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$2$	$x - 2$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x - 2) \cdot (x + 4) = x^{3} + 3 x^{2} - 6 x - 8

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Find the polynomial having roots at −1 , 2 and −4 .

The polynomial generated from the given zeros is: P(x)=x3+3x2−6x−8

Find the polynomial having roots at $- 1$ , $2$ and $- 4$ .

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