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: $P (x) = x^{3} - 3 x^{2} - 13 x + 15$