Find the polynomial having roots at $- 1$ , $2$ , $4$ and $- 9$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 4 x^{3} - 43 x^{2} + 26 x + 72$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$2$	$x - 2$
$4$	$x - 4$
$- 9$	$x + 9$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x - 2) \cdot (x - 4) \cdot (x + 9) = x^{4} + 4 x^{3} - 43 x^{2} + 26 x + 72

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Find the polynomial having roots at −1 , 2 , 4 and −9 .

The polynomial generated from the given zeros is: P(x)=x4+4x3−43x2+26x+72

Find the polynomial having roots at $- 1$ , $2$ , $4$ and $- 9$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} + 4 x^{3} - 43 x^{2} + 26 x + 72$