Turn on thread page Beta
    • Thread Starter
    Offline

    9
    ReputationRep:
    How would I answer this:

    The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

    This is FP1, exam board: Edexcel.
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    How would I answer this:

    The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

    This is FP1, exam board: Edexcel.
    If the quadratic in z doesn't have real roots, what do you know about the discriminant? (from C1)
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Doctor1234)
    How would I answer this:

    The equation (z^2)+bz+11=0, where b is a real number, has distinct non real complex roots. Find the range of possible values of b.

    This is FP1, exam board: Edexcel.
    Well, it's a quadratic with real coefficients. What's the condition on the discriminant that would imply complex roots for this equation?
    • Thread Starter
    Offline

    9
    ReputationRep:
    Erm, we haven't covered discrimants yet.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (Original post by Doctor1234)
    Erm, we haven't covered discrimants yet.
    Should be like one of the first things in C1... maybe even at GCSE.

    The discriminant of a quadratic ax^2+bx+c=0 where a,b,c \in \mathbb \{ \mathbb{R}: a \neq 0 \} is given by b^2-4ac.

    Certain conditions on it determine the amount of real roots that the equation has.
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    Erm, we haven't covered discrimants yet.
    Okay, so I suppose you know the quadratic formula from GCSE:

    x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}.

    Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.

    We call the bit inside the square root, ie b^2-4ac the discriminant.

    Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by K-Man_PhysCheM)
    Okay, so I suppose you know the quadratic formula from GCSE:

    x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}.

    Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.

    We call the bit inside the square root, ie b^2-4ac the discriminant.

    Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
    b^2 has to be less than 44 to obtain a non-real complex number?
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    b^2 has to be less than 44 to obtain a non-real complex number?
    Yes, so what range must b lie between?

    (Hint: sketch the parabola y=x^2 and look for the range of values where the curve lies below the line y=44. This will be a common technique for solving quadratic inequalities in A-level maths /FM)
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by K-Man_PhysCheM)
    Yes, so what range must b lie between?

    (Hint: sketch the parabola y=x^2 and look for the range of values where the curve lies below the line y=44. This will be a common technique for solving quadratic inequalities in A-level maths /FM)
    As long as y is greater than 0 and less than 44?
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    As long as y is greater than 0 and less than 44?
    No, you need to sketch the parabola.

    Let's suppose you had b^2 < 4

    Then sketching y=x^2 and y=4 shows me that the curve is underneath the line between -2 and 2. So in this case, -2<b<2.

    Use the same for your question.
    Attached Images
     
    • Thread Starter
    Offline

    9
    ReputationRep:
    So in my case the curve would be underneath the line + or - root 44?
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    So in my case the curve would be underneath the line + or - root 44?
    Yeah, and that surd can be simplified and should be written as an inequality with b.
    Offline

    9
    ReputationRep:
    (Original post by RDKGames)
    Should be like one of the first things in C1... maybe even at GCSE.

    The discriminant of a quadratic ax^2+bx+c=0 where a,b,c \in \mathbb \{ \mathbb{R}: a \neq 0 \} is given by b^2-4ac.

    Certain conditions on it determine the amount of real roots that the equation has.
    Why do you use notation the OP probably won't understand?
    • TSR Support Team
    Offline

    21
    ReputationRep:
    TSR Support Team
    (Original post by Ano9901whichone)
    Why do you use notation the OP probably won't understand?
    This notation is completely fine for FP1, there’s nothing OP should be unfamiliar with here
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by K-Man_PhysCheM)
    Yeah, and that surd can be simplified and should be written as an inequality with b.
    I see, it makes sense. So it b is out of the range -(sqrt 44) and +(sqrt 44), then the equation would have real roots rather than imaginary roots?
    Offline

    17
    ReputationRep:
    (Original post by Protostar)
    This notation is completely fine for FP1, there’s nothing OP should be unfamiliar with here
    It looks a bit different than how I would format it on paper but yeah you need set notation for the things like solving sets of equations.
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    I see, it makes sense. So it b is out of the range -(sqrt 44) and +(sqrt 44), then the equation would have real roots rather than imaginary roots?
    Yes, that is right.

    Note it should be -2\sqrt{11} < b < 2\sqrt{11}

    and NOT  -2\sqrt{11} \leq b \leq 2\sqrt{11}

    because when b is exactly on the boundary, the quadratic would have one real repeated root.

    PS: it's good practice to always fully simplify surds
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by K-Man_PhysCheM)
    Yes, that is right.

    Note it should be -2\sqrt{11} < b < 2\sqrt{11}

    and NOT  -2\sqrt{11} \leq b \leq 2\sqrt{11}

    because when b is exactly on the boundary, the quadratic would have one real repeated root.

    PS: it's good practice to always fully simplify surds
    My bad.
    Thanks for the help, cleared a lot of confusion. Are you doing A levels or are you at uni?
    Offline

    15
    ReputationRep:
    (Original post by Doctor1234)
    My bad.
    Thanks for the help, cleared a lot of confusion. Are you doing A levels or are you at uni?
    No worries

    I'm in Year 13, so not at Uni yet!
    • Thread Starter
    Offline

    9
    ReputationRep:
    (Original post by K-Man_PhysCheM)
    No worries

    I'm in Year 13, so not at Uni yet!
    Oh kl, well good luck with A2.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 25, 2017

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.