Show that x= -1 is a root of the equation
Hey guys,
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
Scroll to see replies
Original post by BinaryJava
Hey guys,
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
Is there more to the question?
If not, then f(a) = 0 shows that a is a factor
Original post by BinaryJava
Hey guys,
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
For FP1 Exercise 1H, I am told to show that x=-1 is a root of the equation x^3+9x^2+33x+25=0
I subbed in -1 to get 0 and stated that x+1 is a factor.
However I am unsure about how to go on from here. I think it is polynomial division but I don't know how to do it.
-Binary
You have shown that x = -1 is a root by subbing -1 and getting 0. Just announce that it is a root.
Original post by TenOfThem
Is there more to the question?
If not, then f(a) = 0 shows that a is a factor
If not, then f(a) = 0 shows that a is a factor
Hence solve the equation completely
Original post by BinaryJava
Hence solve the equation completely
ok
So, are you saying that you do not know how to find the corresponding quadratic
Original post by BinaryJava
Hence solve the equation completely
Yeah, you need to divide f (x) by (x+1). Have a look at the C2 book, chapter 1 I think, which explains how to divide polynomials.
When you have divided it, you'll get a quadratic which will most likely have complex roots (it is FP1). Just complete the square and it'll be all good.
There will be one real root and two complex roots, which will be conjugates of each other.
Original post by BinaryJava
Hence solve the equation completely
(x+1)(ax^2 +bx +c) multiply out and equate the coefficients to find out what a, b and c is. you should then be able to find out the other 2 roots by factorising or quadratic formula. since its a fp1 question most likely you'd have to use the quadratic formula and the other 2 roots would be complex numbers.
Original post by TenOfThem
ok
So, are you saying that you do not know how to find the corresponding quadratic
So, are you saying that you do not know how to find the corresponding quadratic
Yep, I was thinking about factorizing but I can't see any solution doing this
Original post by BinaryJava
Yep, I was thinking about factorizing but I can't see any solution doing this
There are a number of methods, algebraic long division, recognition, or as Nitrogen says, equating coefficients
Are you familiar with any of this
Original post by KaptainCliff
Yeah, you need to divide f (x) by (x+1). Have a look at the C2 book, chapter 1 I think, which explains how to divide polynomials.
When you have divided it, you'll get a quadratic which will most likely have complex roots (it is FP1). Just complete the square and it'll be all good.
There will be one real root and two complex roots, which will be conjugates of each other.
When you have divided it, you'll get a quadratic which will most likely have complex roots (it is FP1). Just complete the square and it'll be all good.
There will be one real root and two complex roots, which will be conjugates of each other.
My school hasn't looked through the C2 book yet and I don't have one on hand.
Original post by BinaryJava
My school hasn't looked through the C2 book yet and I don't have one on hand.
Is it just easier if I tell you the result is x^2+8x+25?
Original post by KaptainCliff
Is it just easier if I tell you the result is x^2+8x+25?
Don't just give solutions.
Original post by KaptainCliff
Is it just easier if I tell you the result is x^2+8x+25?
How is that going to help the OP the next time he gets one of these problems to solve?
If you'd like to see my (partially) annotated working, I've added a photo. I'm not a teacher, and it's difficult to explain how to divide polynomials on TSR, but this is the best explanation I can offer.
Original post by cambo211
Don't just give solutions.
Original post by KaptainCliff
If you'd like to see my (partially) annotated working, I've added a photo. I'm not a teacher, and it's difficult to explain how to divide polynomials on TSR, but this is the best explanation I can offer.
Don't give solutions, you've already been told.
Original post by james22
Don't give solutions, you've already been told.
I've explained my working.
It's no help if I just explain how to get the result, because there will always be the uncertainty with doing something new in maths. Giving the result just solves things until the OP has been taught how to divide polynomials.
Original post by KaptainCliff
I've explained my working.
It's no help if I just explain how to get the result, because there will always be the uncertainty with doing something new in maths. Giving the result just solves things until the OP has been taught how to divide polynomials.
It's no help if I just explain how to get the result, because there will always be the uncertainty with doing something new in maths. Giving the result just solves things until the OP has been taught how to divide polynomials.
Er, no it doesn't!
The OP needs to learn and practise polynomial division, and then he will have the confidence to tackle the problem by himself
Original post by KaptainCliff
I've explained my working.
It's no help if I just explain how to get the result, because there will always be the uncertainty with doing something new in maths. Giving the result just solves things until the OP has been taught how to divide polynomials.
It's no help if I just explain how to get the result, because there will always be the uncertainty with doing something new in maths. Giving the result just solves things until the OP has been taught how to divide polynomials.
It doesn't matter, the rules are very clear on this. You are not allowed to give full solutions unless as a last resort.
Original post by james22
It doesn't matter, the rules are very clear on this. You are not allowed to give full solutions unless as a last resort.
I didn't know there were rules on helping a person in need.
Original post by KaptainCliff
I didn't know there were rules on helping a person in need.
On the maths forum page there is a post near the top saying "Sticky: Guide to posting in the Maths forum - PLEASE READ BEFORE POSTING!!!", it has all the rules in.
The reason it is banned is because it isn't helping people.
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