Question

The cubic polynomial below has a double root at r4 and one root at x = 6 and passes Through the point (2, 36) as shown. Algebraically determine its equation in factored form. Show how you arrived at your answer.

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Answer 1

The graph in the question is missing.

Answer:

y =
`(-1)/(4)( x^3 + 2x^2 - 32x -96)`

Explanation:

The function is cubic

It has roots as -4, -4 , 6

this means the value of x = -4, -4 , 6 which makes the entire equation zero

so we have solutions as

x+4 = 0

x+4 = 0

x- 6 = 0

on forming a cubic equation using these

(x+4)(x+4)(x-6)

the equation passes through (2,36)

put x = 2

(2+4)(2+4)(2-6) = (6)*(6)*(-4)

which exceeds 36 so we product the equation with -1/4 to get 36

Final equation

y =
`(-1)/(4) (x+4)(x+4)(x-6)`

y =
`(-1)/(4)( x^3 + 2x^2 - 32x -96)`