Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−5. The y-intercept is y=−32.
Find a formula for P(x).

Answer 1

@Directrix

Answer 2

@Mertsj

Answer 3

@jim_thompson5910

Answer 4

@wio

Answer 5

x = 4, x = 4, or x = -5

x - 4 = 0 or x - 4 = 0 or x + 5 = 0

k(x-4)(x-4)(x+5) = 0

k(x-4)(x^2 + x - 20) = 0

k[ x(x^2 + x - 20) - 4(x^2 + x - 20) ] = 0

k( x^3 + x^2 - 20x - 4x^2 - 4x + 80 ) = 0

k( x^3 - 3x^2 - 24x + 80 ) = 0

y = k( x^3 - 3x^2 - 24x + 80 )

Now plug in x = 0 and y = -32 then solve for k

Answer 6

ok thanks

Answer 7

np

Answer 8

i got k=-5/2 and then put it in and got it wrong

Answer 9

@jim_thompson5910

Answer 10

y = k( x^3 - 3x^2 - 24x + 80 )

-32 = k( (0)^3 - 3(0)^2 - 24(0) + 80 )

-32 = 80k

80k = -32

k = -32/80

k = -2/5

so you flipped it somehow

Answer 11

my bad