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

Answer

The polynomial generated from the given zeros is: $P (x) = 2 x^{3} - 11 x^{2} + 17 x - 6$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (2 x - 1) \cdot (x - 2) \cdot (x - 3) = 2 x^{3} - 11 x^{2} + 17 x - 6

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Find the polynomial having roots at 21​ , 2 and 3 .

The polynomial generated from the given zeros is: P(x)=2x3−11x2+17x−6

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

The polynomial generated from the given zeros is: $P (x) = 2 x^{3} - 11 x^{2} + 17 x - 6$