Question

Find a cubic function with the given zeros.

6, -5, 2

Answer 1

(-b/a)x^3 + (c/a)x^2 + (d/a)x + f

Answer 2

Im still not sure how to do this

Answer 3

Can you do it and ill see if i understand all the steps?

Answer 4

\[\alpha x^3 +\beta x^2 + \gamma x +\delta =0\]

Answer 5

how do i know what a b and y are?

Answer 6

The given zeroes:

x = 6
x = -5
x = 2

subtract each number from both sides:

x - 6 = 0
x +5 = 0
x - 2 = 0

Therefore the factors are (x - 6), (x + 5) and (x - 2)

Multiply them together to get the cubic

Answer 7

wait how do i multiply them together?

Answer 8

wait hold on

Answer 9

is this the answer?
f(x) = x3 + 3x2 - 28 + 60

Answer 10

(x - 6)(x + 5) = x(x + 5) - 6(x + 5) = x^2 +5x - 6x - 30 = x^2 -x - 30

x^2 - x - 30(x - 2) = x^2(x - 2) - x(x - 2) - 30(x - 2)
= x^3 - 2x^2 - x^2+ 2x - 30x + 60
= x^3 - 3x^2 - 28x + 60

Answer 11

Yay! i did do it right