Find the polynomial having roots at $- 1$ , $- 5$ and $3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 3 x^{2} - 13 x - 15$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$- 5$	$x + 5$
$3$	$x - 3$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x + 5) \cdot (x - 3) = x^{3} + 3 x^{2} - 13 x - 15

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Find the polynomial having roots at −1 , −5 and 3 .

The polynomial generated from the given zeros is: P(x)=x3+3x2−13x−15

Find the polynomial having roots at $- 1$ , $- 5$ and $3$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} + 3 x^{2} - 13 x - 15$