Find the polynomial having roots at $0$ , $1$ , $5$ and $- 6$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 31 x^{2} + 30 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$1$	$x - 1$
$5$	$x - 5$
$- 6$	$x + 6$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 1) \cdot (x - 5) \cdot (x + 6) = x^{4} - 31 x^{2} + 30 x

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Find the polynomial having roots at 0 , 1 , 5 and −6 .

The polynomial generated from the given zeros is: P(x)=x4−31x2+30x

Find the polynomial having roots at $0$ , $1$ , $5$ and $- 6$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 31 x^{2} + 30 x$