Find the polynomial having roots at $- \frac{1}{4}$ , $\frac{1}{2}$ and $- 2$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 8 x^{3} + 14 x^{2} - 5 x - 2$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- \frac{1}{4}$	$4 x + 1$
$\frac{1}{2}$	$2 x - 1$
$- 2$	$x + 2$

Step 2: Multiply the factors together:

P (x) = (4 x + 1) \cdot (2 x - 1) \cdot (x + 2) = 8 x^{3} + 14 x^{2} - 5 x - 2

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Find the polynomial having roots at −41​ , 21​ and −2 .

The polynomial generated from the given zeros is: P(x)=8x3+14x2−5x−2

Find the polynomial having roots at $- \frac{1}{4}$ , $\frac{1}{2}$ and $- 2$ .

The polynomial generated from the given zeros is: $P (x) = 8 x^{3} + 14 x^{2} - 5 x - 2$