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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{6} - 12 x^{5} + 60 x^{4} - 160 x^{3} + 240 x^{2} - 192 x + 64$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x - 2) \cdot (x - 2) \cdot (x - 2) \cdot (x - 2) \cdot (x - 2) = x^{6} - 12 x^{5} + 60 x^{4} - 160 x^{3} + 240 x^{2} - 192 x + 64

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

The polynomial generated from the given zeros is: P(x)=x6−12x5+60x4−160x3+240x2−192x+64

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

The polynomial generated from the given zeros is: $P (x) = x^{6} - 12 x^{5} + 60 x^{4} - 160 x^{3} + 240 x^{2} - 192 x + 64$