Find a polynomial equation that has zeros at x = 0, x = -5 and x = 6

The answer to your question is x³ + 11² + 30x

Step-by-step explanation:

Data

       x = 0; x = - 5; x = 6

Process

1.- Equal the zeros to zero

      x₁ = 0; x₂ + 5 = 0; x₃ + 6 = 0

2.- Multiply the results

      x(x + 5)(x + 6) = x [ x² + 6x + 5x + 30]

3.- Simplify

                             = x [ x² + 11x + 30]        

4.- Result

                             = x³ + 11² + 30x

x³ - x²- 30x = 0

Step-by-step explanation:

Given that a polynomial has zeros at x = 0, x = -5 and x = 6.

We convert these into factors by rearrange each equation above to convert the equation into the following form:

{expression} = 0

for x = 0    ( x = 0 is the 1st factor. already in correct  form, no further manipulation needed)

for x = -5   (add 5 to both sides)

x + 5 = 0  (x + 5 is the 2nd factor)

for x = 6 (subtract 6 from both sides)

x - 6 = 0 (x - 6 is the 3rd factor)

to obtain the polynomial equation, simply multiply all the factors together and equate to zero, i.e.

(x) · (x+5) · (x-6) = 0

expanding this, we will get

x³ - x²- 30x = 0