Find the polynomial having roots at $1$ , $- \frac{2}{3}$ and $0$ .

Answer

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

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$- \frac{2}{3}$	$3 x + 2$
$0$	$x$

Step 2: Multiply the factors together:

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

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Find the polynomial having roots at 1 , −32​ and 0 .

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

Find the polynomial having roots at $1$ , $- \frac{2}{3}$ and $0$ .

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