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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 4 x^{2} - 11 x + 30$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x - 2) \cdot (x - 5) = x^{3} - 4 x^{2} - 11 x + 30

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

The polynomial generated from the given zeros is: P(x)=x3−4x2−11x+30

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

The polynomial generated from the given zeros is: $P (x) = x^{3} - 4 x^{2} - 11 x + 30$