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: $P (x) = 3 x^{3} - 5 x^{2} - 4 x + 4$