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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 45$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x + 5) \cdot (x - 3) \cdot (x - 1) = x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 45

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

The polynomial generated from the given zeros is: P(x)=x4+4x3−14x2−36x+45

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

The polynomial generated from the given zeros is: $P (x) = x^{4} + 4 x^{3} - 14 x^{2} - 36 x + 45$