Find the polynomial having roots at $- 3$ , $- 1$ , $2$ and $5$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 3 x^{3} - 15 x^{2} + 19 x + 30$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 3$	$x + 3$
$- 1$	$x + 1$
$2$	$x - 2$
$5$	$x - 5$

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x + 1) \cdot (x - 2) \cdot (x - 5) = x^{4} - 3 x^{3} - 15 x^{2} + 19 x + 30

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Find the polynomial having roots at −3 , −1 , 2 and 5 .

The polynomial generated from the given zeros is: P(x)=x4−3x3−15x2+19x+30

Find the polynomial having roots at $- 3$ , $- 1$ , $2$ and $5$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 3 x^{3} - 15 x^{2} + 19 x + 30$