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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 2 x^{2} - 4 x + 8$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$2$	$x - 2$
$- 2$	$x + 2$
$2$	$x - 2$

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x + 2) \cdot (x - 2) = x^{3} - 2 x^{2} - 4 x + 8

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

The polynomial generated from the given zeros is: P(x)=x3−2x2−4x+8

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

The polynomial generated from the given zeros is: $P (x) = x^{3} - 2 x^{2} - 4 x + 8$