Find the polynomial having roots at $2$ , $5$ , $4$ and $1$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 12 x^{3} + 49 x^{2} - 78 x + 40$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$2$	$x - 2$
$5$	$x - 5$
$4$	$x - 4$
$1$	$x - 1$

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x - 5) \cdot (x - 4) \cdot (x - 1) = x^{4} - 12 x^{3} + 49 x^{2} - 78 x + 40

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Find the polynomial having roots at 2 , 5 , 4 and 1 .

The polynomial generated from the given zeros is: P(x)=x4−12x3+49x2−78x+40

Find the polynomial having roots at $2$ , $5$ , $4$ and $1$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 12 x^{3} + 49 x^{2} - 78 x + 40$