Find the polynomial having roots at $- \frac{14}{5}$ , $0$ and $\frac{14}{5}$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 25 x^{3} - 196 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- \frac{14}{5}$	$5 x + 14$
$0$	$x$
$\frac{14}{5}$	$5 x - 14$

Step 2: Multiply the factors together:

P (x) = (5 x + 14) \cdot x \cdot (5 x - 14) = 25 x^{3} - 196 x

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Find the polynomial having roots at −514​ , 0 and 514​ .

The polynomial generated from the given zeros is: P(x)=25x3−196x

Find the polynomial having roots at $- \frac{14}{5}$ , $0$ and $\frac{14}{5}$ .

The polynomial generated from the given zeros is: $P (x) = 25 x^{3} - 196 x$