Find the polynomial having roots at $- 1$ , $- 2$ , $- 3$ and $- 4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 24$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$- 2$	$x + 2$
$- 3$	$x + 3$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x + 2) \cdot (x + 3) \cdot (x + 4) = x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 24

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Find the polynomial having roots at −1 , −2 , −3 and −4 .

The polynomial generated from the given zeros is: P(x)=x4+10x3+35x2+50x+24

Find the polynomial having roots at $- 1$ , $- 2$ , $- 3$ and $- 4$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} + 10 x^{3} + 35 x^{2} + 50 x + 24$