Find the polynomial having roots at $0$ , $10$ , $2$ , $4$ and $- 4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - 12 x^{4} + 4 x^{3} + 192 x^{2} - 320 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$10$	$x - 10$
$2$	$x - 2$
$4$	$x - 4$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 10) \cdot (x - 2) \cdot (x - 4) \cdot (x + 4) = x^{5} - 12 x^{4} + 4 x^{3} + 192 x^{2} - 320 x

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Find the polynomial having roots at 0 , 10 , 2 , 4 and −4 .

The polynomial generated from the given zeros is: P(x)=x5−12x4+4x3+192x2−320x

Find the polynomial having roots at $0$ , $10$ , $2$ , $4$ and $- 4$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - 12 x^{4} + 4 x^{3} + 192 x^{2} - 320 x$