Find the polynomial having roots at $- 3$ , $5$ and $3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 5 x^{2} - 9 x + 45$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 3$	$x + 3$
$5$	$x - 5$
$3$	$x - 3$

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x - 5) \cdot (x - 3) = x^{3} - 5 x^{2} - 9 x + 45

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Find the polynomial having roots at −3 , 5 and 3 .

The polynomial generated from the given zeros is: P(x)=x3−5x2−9x+45

Find the polynomial having roots at $- 3$ , $5$ and $3$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} - 5 x^{2} - 9 x + 45$