Find the polynomial having roots at $1$ , $4$ and $8$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 13 x^{2} + 44 x - 32$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$4$	$x - 4$
$8$	$x - 8$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x - 4) \cdot (x - 8) = x^{3} - 13 x^{2} + 44 x - 32

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Find the polynomial having roots at 1 , 4 and 8 .

The polynomial generated from the given zeros is: P(x)=x3−13x2+44x−32

Find the polynomial having roots at $1$ , $4$ and $8$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} - 13 x^{2} + 44 x - 32$