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

Answer

The polynomial generated from the given zeros is: $P (x) = 4 x^{3} + x^{2} - 27 x + 18$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (4 x - 3) \cdot (x + 3) \cdot (x - 2) = 4 x^{3} + x^{2} - 27 x + 18

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Find the polynomial having roots at 43​ , −3 and 2 .

The polynomial generated from the given zeros is: P(x)=4x3+x2−27x+18

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

The polynomial generated from the given zeros is: $P (x) = 4 x^{3} + x^{2} - 27 x + 18$