Find the polynomial having roots at $\frac{4}{5}$ , $- 3$ and $3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = 5 x^{3} - 4 x^{2} - 45 x + 36$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$\frac{4}{5}$	$5 x - 4$
$- 3$	$x + 3$
$3$	$x - 3$

Step 2: Multiply the factors together:

P (x) = (5 x - 4) \cdot (x + 3) \cdot (x - 3) = 5 x^{3} - 4 x^{2} - 45 x + 36

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Find the polynomial having roots at 54​ , −3 and 3 .

The polynomial generated from the given zeros is: P(x)=5x3−4x2−45x+36

Find the polynomial having roots at $\frac{4}{5}$ , $- 3$ and $3$ .

The polynomial generated from the given zeros is: $P (x) = 5 x^{3} - 4 x^{2} - 45 x + 36$