Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    5x^2+9x+3=0 and 2x^2+x-7=0

    you can't factorise these, how do i solve this non calculator?
    • Very Important Poster
    Offline

    21
    ReputationRep:
    Very Important Poster
    (Original post by tom989)
    5x^2+9x+3=0 and 2x^2+x-7=0

    you can't factorise these, how do i solve this non calculator?
    What other methods do you know for solving quadratics?
    Spoiler:
    Show
    It involves a formula.
    • Thread Starter
    Offline

    0
    ReputationRep:
    quadratic forumla?
    Offline

    15
    (Original post by SeanFM)
    What other methods do you know for solving quadratics?
    Spoiler:
    Show
    It involves a formula.
    Spoiler:
    Show
    Or complete the square.
    • Thread Starter
    Offline

    0
    ReputationRep:
    how would i use complete the square?
    • Very Important Poster
    Offline

    21
    ReputationRep:
    Very Important Poster
    (Original post by tom989)
    quadratic forumla?
    Correct. But you can take your pick between that and the other method suggested
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by tom989)
    how would i use complete the square?
    Let's use a general formula: ax^2 + bx + c = 0
    Step 1 - take a out of the terms involving x: a(x^2+ \frac{bx}{a})+c=0
    Step 2 - look at the x^2+ \frac{bx}{a} divide through by x and divide the second term by 2 (and square the bracket): a(x+ \frac{b}{2a})^2 + c =0
    Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
    Offline

    0
    ReputationRep:
    there are 4 ways to solve quadratics:
    1. Complete the square
    2. the quadratic formula
    3. factorise
    4. graphs (yes you can use graphs to use quadratic)

    You're best choices will be the formula (you find it online) and graphs (but you'll have to use excel to ensure that you get an accurate answer) - input some numbers in the formula and plot an XY scatter graph in excel and take interception of the shape with X line ... it should work very well
    Offline

    20
    ReputationRep:
    (Original post by RAlexO)
    there are 4 ways to solve quadratics:
    1. Complete the square
    2. the quadratic formula
    3. factorise
    4. graphs (yes you can use graphs to use quadratic)

    You're best choices will be the formula (you find it online) and graphs (but you'll have to use excel to ensure that you get an accurate answer) - input some numbers in the formula and plot an XY scatter graph in excel and take interception of the shape with X line ... it should work very well
    You'll rarely get a precise answer solving them graphically, If you include that then you have to include numerical methods as well.
    Also, they're unlikely to be allowed to use Excel in their exam.
    Offline

    0
    ReputationRep:
    (Original post by morgan8002)
    You'll rarely get a precise answer solving them graphically, If you include that then you have to include numerical methods as well.
    Also, they're unlikely to be allowed to use Excel in their exam.
    I did not know he needed it for an exam... I thought it is some sort of homework or essay .
    Offline

    22
    ReputationRep:
    (Original post by Andy98)
    Let's use a general formula: ax^2 + bx + c = 0
    Step 1 - take a out of the terms involving x: a(x^2+ \frac{bx}{a})+c=0
    Step 2 - look at the x^2+ \frac{bx}{a} divide through by x and divide the second term by 2 (and square the bracket): a(x+ \frac{b}{2a})^2 + c =0
    Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
    \displaystyle a\left(x^2 + \frac{bx}{a}\right) + c = 0 \iff a\bigg(\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2}\bigg) + c
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by Zacken)
    \displaystyle a\left(x^2 + \frac{bx}{a}\right) + c = 0 \iff a\bigg(\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2}\bigg) + c
    Oh yeah, oops
    Offline

    22
    ReputationRep:
    (Original post by Andy98)
    Oh yeah, oops
    Which is, by the way, precisely how you derive the quadratic formula.
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by Zacken)
    Which is, by the way, precisely how you derive the quadratic formula.
    It is?
    Offline

    22
    ReputationRep:
    (Original post by Andy98)
    It is?
    \displaystyle a\left(x^2 + \frac{bx}{a}\right) + c = 0 \iff a\bigg(\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2}\bigg) + c = 0

    So, isolating 'x':

    \displaystyle a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} = -c \iff a\left(x + \frac{b}{2a}\right)^2 = \frac{b^2}{4a} - c = \frac{b^2 - 4ac}{4a}

    \displaystyle \iff \left(x + \frac{b}{2a}\right) = \frac{b^2 - 4ac}{4a^2}

    Square rooting and isolating x:

    \displaystyle x = \frac{-b}{2a} \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by Zacken)
    \displaystyle a\left(x^2 + \frac{bx}{a}\right) + c = 0 \iff a\bigg(\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a^2}\bigg) + c = 0

    So, isolating 'x':

    \displaystyle a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} = -c \iff a\left(x + \frac{b}{2a}\right)^2 = \frac{b^2}{4a} - c = \frac{b^2 - 4ac}{4a}

    \displaystyle \iff \left(x + \frac{b}{2a}\right) = \frac{b^2 - 4ac}{4a^2}

    Square rooting and isolating x:

    \displaystyle x = \frac{-b}{2a} \pm \sqrt{\frac{b^2 - 4ac}{4a^2}} = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
    Wow! I never realised that. Nice!
    Offline

    22
    ReputationRep:
    (Original post by Andy98)
    Wow! I never realised that. Nice!
    Learn something new everyday.
    • Study Helper
    • Welcome Squad
    Offline

    18
    ReputationRep:
    Study Helper
    Welcome Squad
    (Original post by Zacken)
    Learn something new everyday.
    True
    Offline

    8
    ReputationRep:
    (Original post by Andy98)
    Let's use a general formula: ax^2 + bx + c = 0
    Step 1 - take a out of the terms involving x: a(x^2+ \frac{bx}{a})+c=0
    Step 2 - look at the x^2+ \frac{bx}{a} divide through by x and divide the second term by 2 (and square the bracket): a(x+ \frac{b}{2a})^2 + c =0
    Step 3 - Take c to the other side, divide through by a, square root the equation and solve for x.
    You have to account for the extra term when the bracket is squared by subtracting (b^2)/4a^2, so in the case of 5x^2 + 9x + 3 = 0 you get:

    5[x^2 + 1.8x + 0.6] = 0
    X^2 + 1.8x + 0.6 = 0
    (X + 0.9)^2 + 0.6 - 0.81 = 0
    (X + 0.9)^2 - 0.21 = 0
    (X + 0.9)^2 = 0.21
    X + 0.9 = +/- sqrt(0.21)
    ∴ x = -0.9 +/- sqrt(0.21)
    Offline

    22
    ReputationRep:
    (Original post by vectorpi)
    You have to account for the extra term when the bracket is squared by subtracting (b^2)/4a^2, so in the case of 5x^2 + 9x + 3 = 0 you get:

    5[x^2 + 1.8x + 0.6] = 0
    X^2 + 1.8x + 0.6 = 0
    (X + 0.9)^2 + 0.6 - 0.81 = 0
    (X + 0.9)^2 - 0.21 = 0
    (X + 0.9)^2 = 0.21
    X + 0.9 = +/- sqrt(0.21)
    ∴ x = -0.9 +/- sqrt(0.21)
    He already knows.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 9, 2015
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
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.