Find the polynomial having roots at $0$ , $4$ and $9$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 13 x^{2} + 36 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$4$	$x - 4$
$9$	$x - 9$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 4) \cdot (x - 9) = x^{3} - 13 x^{2} + 36 x

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Find the polynomial having roots at 0 , 4 and 9 .

The polynomial generated from the given zeros is: P(x)=x3−13x2+36x

Find the polynomial having roots at $0$ , $4$ and $9$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} - 13 x^{2} + 36 x$