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

Answer

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 11 x^{2} + 12 x - 4$

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} - 11 x^{2} + 12 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)=3x3−11x2+12x−4

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

The polynomial generated from the given zeros is: $P (x) = 3 x^{3} - 11 x^{2} + 12 x - 4$