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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{6} - 6 x^{5} + 9 x^{4} + 8 x^{3} - 24 x^{2} + 16$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x - 2) \cdot (x - 2) \cdot (x + 1) \cdot (x + 1) \cdot (x - 2) = x^{6} - 6 x^{5} + 9 x^{4} + 8 x^{3} - 24 x^{2} + 16

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

The polynomial generated from the given zeros is: P(x)=x6−6x5+9x4+8x3−24x2+16

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

The polynomial generated from the given zeros is: $P (x) = x^{6} - 6 x^{5} + 9 x^{4} + 8 x^{3} - 24 x^{2} + 16$