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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 5 x^{3} - 10 x^{2} + 80 x - 96$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 3) \cdot (x - 4) \cdot (x - 2) \cdot (x + 4) = x^{4} - 5 x^{3} - 10 x^{2} + 80 x - 96

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

The polynomial generated from the given zeros is: P(x)=x4−5x3−10x2+80x−96

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

The polynomial generated from the given zeros is: $P (x) = x^{4} - 5 x^{3} - 10 x^{2} + 80 x - 96$