Find the polynomial having roots at $- 1$ , $0$ , $3$ and $5$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 7 x^{3} + 7 x^{2} + 15 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$0$	$x$
$3$	$x - 3$
$5$	$x - 5$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot x \cdot (x - 3) \cdot (x - 5) = x^{4} - 7 x^{3} + 7 x^{2} + 15 x

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Find the polynomial having roots at −1 , 0 , 3 and 5 .

The polynomial generated from the given zeros is: P(x)=x4−7x3+7x2+15x

Find the polynomial having roots at $- 1$ , $0$ , $3$ and $5$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 7 x^{3} + 7 x^{2} + 15 x$