Polynomial Q (1 Viewer)

[shaon0]

a) x^3-9x^2+24x+k=0 has two equal roots.
i) find the possible k values.

I tried but i can't get a value for k.

 

[tommykins]

回复: Polynomial Q

Hint : Differentiate.

 

[lolokay]

Spoiler

if you differentiate that you get 3x² - 18x + 8 = 0
x = 2, 4
A double root must occur at one of these (it must be a min/max)
subbing these into the original equation gives k = -20, -16

yeah, just use the hint ^

 

[tommykins]

回复: Re: Polynomial Q

Let the roots be @, @
Sum of roots = @+@=9
@=4.5
Product of Roots = @2=-k
k=-(4.5)2

It's a cubic mate

 

[12o9]

yeah i just realised =p sorry.

 

[shaon0]

Spoiler

if you differentiate that you get 3x² - 18x + 8 = 0
x = 2, 4
A double root must occur at one of these (it must be a min/max)
subbing these into the original equation gives k = -20, -16

yeah, just use the hint ^

But in the question it says not to use calculus or you shouldn't use calculus. i did it with calculus before.
Thanks for the help, first in MX2. (At this rate, if i get MX2; i will come last in the state. )

 

[tommykins]

回复: Re: Polynomial Q

Okay.

2a+b = 9
2ab + a^2 = 24

b = 9-2a

2a(9-2a) + a^2 =24
18a - 4a^2+a^2 = 24
3a^2 - 18a + 24 = 0
a^2 - 6a + 8 = 0
(a-4)(a-2) = 0

a = 2, 4.

Sub these into eqn to find k.

 

[shaon0]

Re: 回复: Re: Polynomial Q

Already did it, but thanks for your help