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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 29 x^{2} + 30 x$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x + 5) \cdot x \cdot (x - 1) \cdot (x - 6) = x^{4} - 2 x^{3} - 29 x^{2} + 30 x

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

The polynomial generated from the given zeros is: P(x)=x4−2x3−29x2+30x

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

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 29 x^{2} + 30 x$