Find the polynomial having roots at $- 1$ , $3$ , $0$ and $0$ .

Answer

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

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$3$	$x - 3$
$0$	$x$
$0$	$x$

Step 2: Multiply the factors together:

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

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Find the polynomial having roots at −1 , 3 , 0 and 0 .

The polynomial generated from the given zeros is: P(x)=x4−2x3−3x2

Find the polynomial having roots at $- 1$ , $3$ , $0$ and $0$ .

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