Find the polynomial having roots at $\frac{1}{4}$ , $- 2$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 4 x^{3} + 19 x^{2} + 19 x - 6$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$\frac{1}{4}$	$4 x - 1$
$- 2$	$x + 2$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

P (x) = (4 x - 1) \cdot (x + 2) \cdot (x + 3) = 4 x^{3} + 19 x^{2} + 19 x - 6

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Find the polynomial having roots at 41​ , −2 and −3 .

The polynomial generated from the given zeros is: P(x)=4x3+19x2+19x−6

Find the polynomial having roots at $\frac{1}{4}$ , $- 2$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = 4 x^{3} + 19 x^{2} + 19 x - 6$