Hey there! Sign in to join this conversationNew here? Join for free

Factorising quadratic equations help please.... Watch

    • Thread Starter
    Offline

    0
    ReputationRep:
    Whats the best way to find the value of n by factorising?
    3n^2 - 2n - 7400 = 0
    • Study Helper
    Online

    13
    (Original post by Nkhan)
    Whats the best way to find the value of n by factorising?
    3n^2 - 2n - 7400 = 0
    That's one way, or the formula.
    Offline

    17
    ReputationRep:
    (Original post by Nkhan)
    Whats the best way to find the value of n by factorising?
    3n^2 - 2n - 7400 = 0
    Note that when you plug n=50 into the equation, you find that the LHS=RHS=0. This means that (n-50) is a factor.

    So you have:
    3n^2-2n-7400=(n-50)(3n+B)=3n^2-(150+B)n-50B

    By comparing both sides, you can see that:
    150+B=2
    and
    50B=7400

    Therefore B=148 so:

     3n^2-2n-7400=(n-50)(3n+148)=0

    If you can't spot that factorisation immediately, then complete the square (or if you have calculator on hand, the quadratic formula).
    Offline

    0
    ReputationRep:
    multiply -7400 by 3 to get -22200
    then find two numbers which have a difference of -2 and multiple to get -22200
    so 148 and -150 :
    3n^2 - 150n + 148n - 7400

    look at the first part separately to the second part
    3n^2 - 150n
    take out the common factor of 3n
    3n(n-50)

    and do the same on the second part:
    148(n-50) ---> both brackets show be equal

    then you end up with 3n(n-50) + 148(n-50)
    so (3n+148)(n-50)
    this makes n= 50 and -49.333


    hpe this helps!
    Offline

    0
    ReputationRep:
    multiply -7400 by 3 to get -22200
    then find two numbers which have a difference of -2 and multiple to get -22200
    so 148 and -150 :
    3n^2 - 150n + 148n - 7400

    look at the first part separately to the second part
    3n^2 - 150n
    take out the common factor of 3n
    3n(n-50)

    and do the same on the second part:
    148(n-50) ---> both brackets show be equal

    then you end up with 3n(n-50) + 148(n-50)
    so (3n+148)(n-50)
    this makes n= 50 and -49.333

    hpe this helps!
    Offline

    0
    ReputationRep:
    Method for almost any quadratic equation is to find two numbers which...
    - When multiplied together give the coefficient of the squared number multiplied by the added/subtracted number...
    - And when added give the coefficient of the number on its own (technically to the power of one)

    So as $Jellybeans$ said above you need to find two numbers which multiply to give -22200 and add to give 2. As the multiplied number is a negative you will know that one of these two numbers will be negative (confirmed by the very low -2n in contrast).
    So with a bit of trial and error (i usually test a few numbers on some rough paper) you'll find the two numbers you need are 148 and -150 (multiply to give -22200 and add to give 2) and then you can follow through the answer above to get the final solution.

    Alternatively if this method does not work (i.e. it is difficult to see an obvious solution) you can use the quadratic formula...

    x = -b (+ or -) [squ root(b^2 - 4ac)]/[2a] <---- don't know how to do the symbols but if you type in quadratic formula into google it will come up for you.

    Then you assign your a, b and c vals..
    So...
    a= 3
    b = -2
    c= -7400

    and then put these all into the equation and work out for x (Don't forget to find the TWO roots (+ or -))
    This method may take a while so to test there are solutions at all sub your a,b,c vals into the (-b^2 - 4ac). If the outcome is negative, you know there are no solutions.
    • Study Helper
    Online

    13
    (Original post by Farhan.Hanif93)
    Note that when you plug n=50 into the equation, you find that the LHS=RHS=0. This means that (n-50) is a factor.
    What would prompt you to check n=50?
    Offline

    17
    ReputationRep:
    (Original post by ghostwalker)
    What would prompt you to check n=50?
    Well it was a guess. I knew that if I'm looking for a positive root then 3 times the square of that root must be larger than 7400. From there, n=50 was an obvious first choice. Also following that, the dead giveaway was that 50 is a factor of 7400.
    Offline

    0
    ReputationRep:
    (Original post by ghostwalker)
    What would prompt you to check n=50?
    I guess it's just intuitive, try educated guesses
    Offline

    0
    ReputationRep:
    (Original post by ghostwalker)
    What would prompt you to check n=50?
    I'd say the -2 in the middle is roughly zero so one of our numbers is roughly 3 times the other. Since their product is 7400 on of them is roughly \sqrt{\frac{7400}{3}} so I'd say one of them is about 50.

    This works quite well in these cases.

    Edit. LaTeX typo.
  1. See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

Poll
Did TEF Bronze Award affect your UCAS choices?
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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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