Polynomial Question Help (: (1 Viewer)

[lisarh]

Hey guys, can anyone help me with these tricky questions.

 

[lyounamu]

Hey guys, can anyone help me with these tricky questions.

1) Maximum & minimum points occur when dy/dx = 0

i.e. when 3x^2 + 2ax + b = 0

Using the quadratic formula:

x = (-2a +- (plus and minus) SQRT (4a^2 - 4 . 3 . b))/6

So there are two (maximum and minimum) points.

x = (-2a + SQRT (4a^2 - 12b))/6 and (-2a - SQRT (4a^2 - 12b))/6

Add them up together, you get -4a/6 = -2a/3

Therefore, @ + $ (the roots) = -2a/3

2) point of inflexion is at d^2y/dx^2 = 0
i.e. 6x + 2a = 0
6x = -2a
x= -a/3 which is essentially -(2a/3)/2 = (@+$)/2

 

[Dr. Zoidberg]

 

[lyounamu]

Hey guys, can anyone help me with these tricky questions.

3. Let the roots be @, 1/@ and $

@ . 1/@ . $ = -d/a
Therefore, $ = -b


@ . 1/@ + @ . $ + $ . 1/@ = c/a
1 + -b@ + -b/@ = 0
-b(@+1/@) = -1
(@+1/@) = 1/b


And NOW,
@ + 1/@ + $ = -b/a
@ + 1/@ - b = -a
1/b - b = -a
a = b - 1/b

 

[lisarh]

Thanks for the help lyounamu & Dr. Zoidberg! ^^
:wave:

 

[lisarh]

While you're at it, can you do this too?
Thanks

 

[M@ster P]

is this from a past paper or from a textbook out of curiosity?

 

[lisarh]

Its random tutor homework questions. My teacher gets them from all over the place. So, its most probably past paper questions.

 

[12o9]

is this from a past paper or from a textbook out of curiosity?

They're past catholic paper questions.

 

[tommykins]

回复: Re: Polynomial Question Help

While you're at it, can you do this too?
Thanks

f(1) = 0
f'(1) = 0
f(-1) = -4

Solve all from there, simulatenous equations.