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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 9 x^{3} + 18 x^{2} + 32 x - 96$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x + 2) \cdot (x - 3) \cdot (x - 4) \cdot (x - 4) = x^{4} - 9 x^{3} + 18 x^{2} + 32 x - 96

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

The polynomial generated from the given zeros is: P(x)=x4−9x3+18x2+32x−96

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

The polynomial generated from the given zeros is: $P (x) = x^{4} - 9 x^{3} + 18 x^{2} + 32 x - 96$