Year 12- Polynomials Help (1 Viewer)

[shaon0]

Could someone help me with:
This is from the Year 12: 3unit Cambridge textbook.

 

[shaon0]

Doesn't the document open?

 

[lyounamu]

Could someone help me with:
This is from the Year 12: 3unit Cambridge textbook.

9a)
x^3 - 6x^2 + ax + b = 0 when we substitue x = 3 or x = -1 (since x+1 and x-3 are the factors of the equation)

3^3 - 6(3)^2 + 3a + b = 0
27 - 54 + 3a + b = 0 ...(1)

And

-1^3 - 6(-1)^2 + a + b = 0
-1 - 6 - a + b = 0 ...(2)

Solve them simultaneously to find the value of a.

(2) - (1): -20 + 4a = 0
Therefore, a = 5. Substitute a = 5 into the equation (1),
Therefore, you get b = 12

Since you found a & b you can work out the 2nd part easily. It's all about division method now.

9b)
Substitute x = -2 and x = 4 on two different occasions so you can get 2 equations.
2x^3 + ax^2 - 14x + b = 0
2(-2)^3 + a(-2)^2 - 14 . -2 + b = 0
-16 + 4a + 28 + b = 0 ...(1)

And
2x^3 + ax^2 -14x + b = 0
2(4)^3 + a(4)^2 - 14 . 4 + b = 0
128 + 16a - 56 + b = 0 ...(2)

Work them simulatenously.

(2) - (1): 12 a + 60 = 0
So a = -5. And you get b = 8 if you substitute a = -5 into the equation (1).

13(a)
Guess & check:
P(1) = 4 . 1^3 - 8 . 1^2 - 3.1 + 9 =2
Therefore, 1 is not a root
P(-1) = 4. -1^3 - 8(-1)^2 - 3 . -1 + 9 = 0
So, -1 is a root.

Divide 4x^3 - 8x^2 -3x + 9 =0 by (x+1)

So you get 4x^3 - 8x^2 - 3x + 9 = (4x^2 - 12x +9)(x+1)
= (2x-3)(2x-3)(x+1)

So the roots are 3/2, 3/2 and -1.

 

[shaon0]

You substituted the wrong values for x in part 9a)
Thanks for the help.

 

[lyounamu]

You substituted the wrong values for x in part 9a)
Thanks for the help.

No, I didn't. I put that a=3 and I got b=12.

Work it out yourself. You will get that. And I am sure it's right. (even though I wrote straight on the computer).

Your questions are all in the same type. I think 13b), 13c) and 13d) all require same way of working out. Hope that helped.

 

[midifile]

No, I didn't. I put that a=3 and I got b=12.

Work it out yourself. You will get that. And I am sure it's right. (even though I wrote straight on the computer).

He just got confused because at the begining you wrote "substitute x=-3 or x=1" and then you substituted x=3 and x=-1 (which you were meant to)

 

[shaon0]

No, I didn't. I put that a=3 and I got b=12.

Work it out yourself. You will get that. And I am sure it's right. (even though I wrote straight on the computer).

Your questions are all in the same type. I think 13b), 13c) and 13d) all require same way of working out. Hope that helped.

yea thats right... I used the same method but i kept making silly mistakes before which i overlooked. Thanks
Fiinished all of them...Thanks for the help.

 

[lyounamu]

He just got confused because at the begining you wrote "substitute x=-3 or x=1" and then you substituted x=3 and x=-1 (which you were meant to)

Hahahahaha...

Sorry for that Shaon. I wrote that straight on computer and I was quite brain-damamged at that time you know (from doing 3 hours of study straight for a subject apart from maths).

 

[shaon0]

Hahahahaha...

Sorry for that Shaon. I wrote that straight on computer and I was quite brain-damamged at that time you know (from doing 3 hours of study straight for a subject apart from maths).

No worries....i have finished all the Questions on that section from the Year 12 Polynomials. Wasn't that hard to be honest...i kept making the same stupid mistakes though. Thanks for your help.

 

[lyounamu]

No worries....i have finished all the Questions on that section from the Year 12 Polynomials. Wasn't that hard to be honest...i kept making the same stupid mistakes though. Thanks for your help.

That's great. I wish you luck in the next exam. You are sure to nail it at this rate.

 

[shaon0]

That's great. I wish you luck in the next exam. You are sure to nail it at this rate.

Thanks but i'll probably forget everything...i have a bad memory.
Anyways thanks for the help. I have a test on Week 2 Term 3 for maths so i have to get 100%