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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + x^{3} - 22 x^{2} - 16 x + 96$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x - 4) \cdot (x + 4) \cdot (x + 3) = x^{4} + x^{3} - 22 x^{2} - 16 x + 96

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

The polynomial generated from the given zeros is: P(x)=x4+x3−22x2−16x+96

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

The polynomial generated from the given zeros is: $P (x) = x^{4} + x^{3} - 22 x^{2} - 16 x + 96$