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

Answer

The polynomial generated from the given zeros is: $P (x) = 2 x^{2} + 7 x + 3$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (2 x + 1) = 2 x^{2} + 7 x + 3

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Find the polynomial having roots at −3 and −21​ .

The polynomial generated from the given zeros is: P(x)=2x2+7x+3

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

The polynomial generated from the given zeros is: $P (x) = 2 x^{2} + 7 x + 3$