Find the polynomial having roots at $- 1$ , $2$ , $- 8$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 10 x^{3} + 11 x^{2} - 46 x - 48$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$2$	$x - 2$
$- 8$	$x + 8$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x - 2) \cdot (x + 8) \cdot (x + 3) = x^{4} + 10 x^{3} + 11 x^{2} - 46 x - 48

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Find the polynomial having roots at −1 , 2 , −8 and −3 .

The polynomial generated from the given zeros is: P(x)=x4+10x3+11x2−46x−48

Find the polynomial having roots at $- 1$ , $2$ , $- 8$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} + 10 x^{3} + 11 x^{2} - 46 x - 48$