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

Answer

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} + 5 x^{2} - 3 x - 2$

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} + 5 x^{2} - 3 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+5x2−3x−2

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

The polynomial generated from the given zeros is: $P (x) = 6 x^{3} + 5 x^{2} - 3 x - 2$