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

Answer

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

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (3 x + 2) \cdot (x - 1) \cdot (x + 2) = 3 x^{3} + 5 x^{2} - 4 x - 4

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Find the polynomial having roots at −32​ , 1 and −2 .

The polynomial generated from the given zeros is: P(x)=3x3+5x2−4x−4

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

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