This discussion is now closed.

Check out other Related discussions

- Cardiff Award - what is it? Worth it?
- UEA grading
- TSR News Quiz of the Week #151 (15 June 2024) *Manifesto week special*
- The School Dux
- TSR News Quiz of the Week #146 (4 May 2024) *Local elections special!*
- TSR News Quiz of the Week #139 (9 March 2024)
- If i do foundation Chemistry, will it affect me later on in life?
- Access Course into Science
- Locker rentals at Sir Tom Finney Sports Centre
- TSR Quiz of the Week #140 - Photo edit round!
- TSR Community Awards 2023 Winners
- Grading system
- UCLan foundation year, live at home or accommodations?
- TSR News Quiz #155 (7th July 2024) *General election bonus quiz*
- University of Essex - Sports Question
- Where to Study Nursing
- Having trouble with my A-Level decisions..
- TSR News Quiz #128 (18 November 2023)
- TSR News Quiz of the Week #159 (3rd Aug 2024)
- what do i do??

Worked Solution:

y = 2x2 + px + q

When x=(1+√3) and y=(5√3):

5√3 = 2(1+√3)² + p(1+√3) + q

5√3 = 2(1+√3)(1+√3) + p(1+√3) + q

5√3 = 2[1+2√3+3] + p(1+√3) + q

5√3 = 2 + 4√3 + 6 + p + √3.p + q

5√3 = 8 + 4√3 + p + √3.p + q

5√3 = √3(4+p) + 8 + p + q

Equating constants:

5 = 4 + p

p = 1

and:

0 = 8 + p + q

Substitute p:

0 = 8 + 1 + q

0 = 9 + q

q = -9

p = 1, q = -9

y = 2x2 + px + q

When x=(1+√3) and y=(5√3):

5√3 = 2(1+√3)² + p(1+√3) + q

5√3 = 2(1+√3)(1+√3) + p(1+√3) + q

5√3 = 2[1+2√3+3] + p(1+√3) + q

5√3 = 2 + 4√3 + 6 + p + √3.p + q

5√3 = 8 + 4√3 + p + √3.p + q

5√3 = √3(4+p) + 8 + p + q

Equating constants:

5 = 4 + p

p = 1

and:

0 = 8 + p + q

Substitute p:

0 = 8 + 1 + q

0 = 9 + q

q = -9

p = 1, q = -9

IZZY!

i repped the first person to reply. i ll rep again if some1 explains why do you get

5√3 = √3(4+p) + 8 + p + q

and then

5 = 4 + p

thanks.

the bear remind me later, like in 2 days and i ll rep u lol.

5√3 = √3(4+p) + 8 + p + q

and then

5 = 4 + p

thanks.

the bear remind me later, like in 2 days and i ll rep u lol.

The left hand side must equal the right hand side, as with all equations.

By inspection, it is clear that there is a 'coefficient' for √3 of 5 on the left hand side. On the right hand side, there is also a 'coefficient' of √3 of (4+q). These must be equal, so you get:

5 = 4 + p

There is nothing else on the left hand side but still 8 + p + q on the right hand side, so therefore it follows that also:

0 = 8 + p + q

steve2005

I don't understand the end bit .

I presume 'rep' means reputation and ' u ' means you : that's easy but what about ' lol.'

I presume 'rep' means reputation and ' u ' means you : that's easy but what about ' lol.'

I'm fairly sure that 'lol' is supposed to be an abbreviation for 'laugh out loud' though the vast majority of people don't actually laugh at all when they say 'lol'.

please help again.solve this.

a Show that

(x^{2} + 2x − 3)(x^{2} − 3x − 4) ≡ x^{4} − x^{3} − 13x^{2} + x + 12.

b Hence solve the equation

x^{4} − x^{3} − 13x^{2} + x + 12 = 0.

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

a Show that

(x

b Hence solve the equation

x

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

IZZY!

please help again.solve this.

a Show that

(x^{2} + 2x − 3)(x^{2} − 3x − 4) ≡ x^{4} − x^{3} − 13x^{2} + x + 12.

b Hence solve the equation

x^{4} − x^{3} − 13x^{2} + x + 12 = 0.

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

a Show that

(x

b Hence solve the equation

x

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

For part (b) use the result obtained in part (a) and the fact that if f(x)g(x)=0 then f(x)=0 or g(x)=0 (or both).

IZZY!

please help again.solve this.

a Show that

(x^{2} + 2x − 3)(x^{2} − 3x − 4) ≡ x^{4} − x^{3} − 13x^{2} + x + 12.

b Hence solve the equation

x^{4} − x^{3} − 13x^{2} + x + 12 = 0.

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

a Show that

(x

b Hence solve the equation

x

i ve done the a part.i cant do the b part.help is greatly appreciated and will be awarded with rep, if you remind me later.

having done a by expanding it, you know x^4... is divisible by those 2 factors. hmm. but can those factors also be broken down into factors? this will give you the fully factorised expression of x^4... and you should know how to find the roots from that.

- Cardiff Award - what is it? Worth it?
- UEA grading
- TSR News Quiz of the Week #151 (15 June 2024) *Manifesto week special*
- The School Dux
- TSR News Quiz of the Week #146 (4 May 2024) *Local elections special!*
- TSR News Quiz of the Week #139 (9 March 2024)
- If i do foundation Chemistry, will it affect me later on in life?
- Access Course into Science
- Locker rentals at Sir Tom Finney Sports Centre
- TSR Quiz of the Week #140 - Photo edit round!
- TSR Community Awards 2023 Winners
- Grading system
- UCLan foundation year, live at home or accommodations?
- TSR News Quiz #155 (7th July 2024) *General election bonus quiz*
- University of Essex - Sports Question
- Where to Study Nursing
- Having trouble with my A-Level decisions..
- TSR News Quiz #128 (18 November 2023)
- TSR News Quiz of the Week #159 (3rd Aug 2024)
- what do i do??

Latest

Trending