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

Answer

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} - 13 x^{2} + 9 x - 2$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (3 x - 2) \cdot (2 x - 1) \cdot (x - 1) = 6 x^{3} - 13 x^{2} + 9 x - 2

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Find the polynomial having roots at 32​ , 21​ and 1 .

The polynomial generated from the given zeros is: P(x)=6x3−13x2+9x−2

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

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} - 13 x^{2} + 9 x - 2$