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

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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