Find the polynomial having roots at $5$ , $2$ , $3$ and $0$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 10 x^{3} + 31 x^{2} - 30 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$5$	$x - 5$
$2$	$x - 2$
$3$	$x - 3$
$0$	$x$

Step 2: Multiply the factors together:

P (x) = (x - 5) \cdot (x - 2) \cdot (x - 3) \cdot x = x^{4} - 10 x^{3} + 31 x^{2} - 30 x

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Find the polynomial having roots at 5 , 2 , 3 and 0 .

The polynomial generated from the given zeros is: P(x)=x4−10x3+31x2−30x

Find the polynomial having roots at $5$ , $2$ , $3$ and $0$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 10 x^{3} + 31 x^{2} - 30 x$