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

Answer

The polynomial generated from the given zeros is: $P (x) = 6 x^{4} + 23 x^{3} + 28 x^{2} + 13 x + 2$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (2 x + 1) \cdot (3 x + 1) \cdot (x + 1) \cdot (x + 2) = 6 x^{4} + 23 x^{3} + 28 x^{2} + 13 x + 2

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Find the polynomial having roots at −21​ , −31​ , −1 and −2 .

The polynomial generated from the given zeros is: P(x)=6x4+23x3+28x2+13x+2

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

The polynomial generated from the given zeros is: $P (x) = 6 x^{4} + 23 x^{3} + 28 x^{2} + 13 x + 2$