Find the polynomial having roots at $8$ , $- 5$ , $5$ and $0$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 8 x^{3} - 25 x^{2} + 200 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$8$	$x - 8$
$- 5$	$x + 5$
$5$	$x - 5$
$0$	$x$

Step 2: Multiply the factors together:

P (x) = (x - 8) \cdot (x + 5) \cdot (x - 5) \cdot x = x^{4} - 8 x^{3} - 25 x^{2} + 200 x

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Find the polynomial having roots at 8 , −5 , 5 and 0 .

The polynomial generated from the given zeros is: P(x)=x4−8x3−25x2+200x

Find the polynomial having roots at $8$ , $- 5$ , $5$ and $0$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 8 x^{3} - 25 x^{2} + 200 x$