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

Answer

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

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

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

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

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

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

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