Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    Three questions I am not totally sure how to solve I could do with some help on.

    1) Solve the equation 2x^2+32x+119=0
    write you answers in the form p+q√2 where p and q are rational numbers.

    I completed the square (not totally sure that this is right) and got 2(x+8)^2-9=0. Then 2x+16=3 so x+8=3/2 but don't know if this is right or what to do next.

    Secondly, I am stuck on this

    1)Express x^2-12x+40 in the form (x-p)^2+q. I did this and got (x-6)^2+4.
    but then, in part b it says find the least value of x^2-12x+40 and I am not totally sure of what this means.

    3)Lastly, I am having trouble with this. Find the constant a,b and c such that, for all values of x,
    3x^2-6x+10=a(x+b)^2+c.

    Now I completed the square on it but not sure what to do next.

    Any helo will be much appreciated.
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by stefl14)
    Three questions I am not totally sure how to solve I could do with some help on.

    1) Solve the equation 2x^2+32x+119=0
    write you answers in the form p+q√2 where p and q are rational numbers.

    I completed the square (not totally sure that this is right) and got 2(x+8)^2-9=0. Then 2x+16=3 so x+8=3/2 but don't know if this is right or what to do next.
    TSR is horrendously slow at present; perhaps they're doing their upgrade.

    Anyhow, lets start with number 1.

    You're correct up to "2(x+8)^2-9=0"

    Now you need to find x.

    What you had wasn't correct, although it had some good elements in it. Post your working there after and we can see what you were doing.
    Offline

    8
    ReputationRep:
    (Original post by stefl14)
    Three questions I am not totally sure how to solve I could do with some help on.

    1) Solve the equation 2x^2+32x+119=0
    write you answers in the form p+q√2 where p and q are rational numbers.

    I completed the square (not totally sure that this is right) and got 2(x+8)^2-9=0. Then 2x+16=3 so x+8=3/2 but don't know if this is right or what to do next.

    Secondly, I am stuck on this

    1)Express x^2-12x+40 in the form (x-p)^2+q. I did this and got (x-6)^2+4.
    but then, in part b it says find the least value of x^2-12x+40 and I am not totally sure of what this means.

    3)Lastly, I am having trouble with this. Find the constant a,b and c such that, for all values of x,
    3x^2-6x+10=a(x+b)^2+c.

    Now I completed the square on it but not sure what to do next.

    Any helo will be much appreciated.
    Hello,

    1)Your completing is right, then add both side 9 then divide by 2
    Taking the root |x+8|=\frac{3}{\sqrt{2}} rationalize
    the denominator at the right side
    Solve if a) x>=-8 b) x<-8
    2)You are right: (x-6)^2+4
    Consider that it is a function, and taking any value into x and calculating, you get the value of function at that x location. This type of quaratic function is a parabola, which has so called stationary point.
    It is that point where the parabola change direction. It is minimum (least value) or maximum (greatest value) depending on the sign of the quadratic term.
    In you example the sign is postive, so this function has minimum.
    The equation if the parabola: Y-y0=1/(2p)(X-x0)^2 where
    (x0,y0) is cooordinates of the vertex (the stationary point).
    So Y=(x-6)^2+4 -> x0=6 y0=4
    Your least value is 4, the location is 6.
    3. Complete the left side of the equation an compare coefficients of
    both side and read the values.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: September 30, 2010

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.