Find the polynomial having roots at $2$ , $- 3$ and $- 1$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 2 x^{2} - 5 x - 6$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$2$	$x - 2$
$- 3$	$x + 3$
$- 1$	$x + 1$

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x + 3) \cdot (x + 1) = x^{3} + 2 x^{2} - 5 x - 6

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Find the polynomial having roots at 2 , −3 and −1 .

The polynomial generated from the given zeros is: P(x)=x3+2x2−5x−6

Find the polynomial having roots at $2$ , $- 3$ and $- 1$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} + 2 x^{2} - 5 x - 6$