Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

show that the line... does not intersect at the curve... ?

Announcements Posted on
Will you get the grades you need for uni? Get prepared today and de-stress, sign up to email alerts for course places! 02-06-2015
Waiting on IB results? Our IB results hub explains everything you need to know 01-06-2015
  1. Offline

    ReputationRep:
    hi

    show that the the line y=4x+1 does not intersect the curve y=x^2 +5x+2

    is this just a simultaneous equation?

    part b says
    find the values of m such that the line y=mx+1 meets the curve y=x^2 +5x+2 at exactly one point

    what the heck do i do for this
  2. Offline

    ReputationRep:
    Try to form a quadratic. Now take the discriminant. What does the fact that the discriminant is negative tell you?

    Part b

    What does the discriminant need to be now so that there is only one root?
  3. Offline

    ReputationRep:
    (Original post by Mr M)
    Try to form a quadratic. Now take the discriminant. What does the fact that the discriminant is negative tell you?

    Part b

    What does the discriminant need to be now so that there is only one root?
    negative discriminant means there's no real roots.
    discriminant has be greater than zero for it to have one root?
  4. Offline

    ReputationRep:
    Actually, it has to be 0.
  5. Offline

    ReputationRep:
    (Original post by hamzah190)
    negative discriminant means there's no real roots.
    discriminant has be greater than zero for it to have one root?
    Well it this case it means the line and curve do not intersect.

    Discriminant = zero if there is a single point of intersection.
  6. Offline

    ReputationRep:
    (Original post by hamzah190)
    negative discriminant means there's no real roots.
    discriminant has be greater than zero for it to have one root?
    hmm, I did 4x+1=x^2 +5x+2
    and managed to get x^2+x+1
    cant put that into a quadratic formula, can I ?
  7. Offline

    ReputationRep:
    (Original post by hamzah190)
    hmm, I did 4x+1=x^2 +5x+2
    and managed to get x^2+x+1
    cant put that into a quadratic formula, can I ?
    Do you know what the discriminant is?
  8. Offline

    ReputationRep:
    (Original post by Mr M)
    Do you know what the discriminant is?
    b^2 -4ac

    do i sub x^2 + x + 1 into the discriminant? (still on part a)
  9. Offline

    ReputationRep:
    (Original post by hamzah190)
    b^2 -4ac

    do i sub x^2 + x + 1 into the discriminant? (still on part a)
    yes
  10. Offline

    ReputationRep:
    (Original post by TenOfThem)
    yes
    so i got 1^2 -4(1)(1)

    which is -3

    what do i do now
  11. Offline

    ReputationRep:
    (Original post by hamzah190)
    so i got 1^2 -4(1)(1)

    which is -3

    what do i do now
    That shows that there are no real roots. Therefore the two lines don't intersect. End of part a.
  12. Offline

    ReputationRep:
    (Original post by 117r)
    That shows that there are no real roots. Therefore the two lines don't intersect. End of part a.
    hmm, how do i do part b

    do i just put the -3 from part a and sub into y=mx+1 so y=m-3+1
  13. Offline

    ReputationRep:
    What you need to do is set b^2-4ac = 0, then solve to find those values, using your previous equations.
  14. Offline

    ReputationRep:
    (Original post by hamzah190)
    hmm, how do i do part b

    do i just put the -3 from part a and sub into y=mx+1 so y=m-3+1
    No. You make the discriminant equal 0 to find b when the lines intersect at one point.

    b^2 - 4(1)(1) = 0
    b^2 -4=0
    b^2=4
    b = 2 or -2

    So now you know that x^2 +/-2x +1 has one real root.

    Also x^2 + 5x +2 = x^2 +/-2x +1 + mx + 1
    (This is from the beginning, where you had 4x+1=x^2 + 5x +2 and you subtracted 4x+1 from both sides. You know you want x^2 + 5x +2 - 4x +1 to equal x^2 +/-2x +1 (for in this instance there is one root), so Also x^2 + 5x +2 = x^2 +/-2x +1 + mx + 1)

    Therefore m = 7 or 3
  15. Offline

    ReputationRep:
    I think you need to speak to your teacher now hamzah. We can teach you a mechanical process but, with absolutely no understanding, there is little chance you will ever be able to apply it.
  16. Offline

    ReputationRep:
    (Original post by 117r)
    No. You make the discriminant equal 0 to find b when the lines intersect at one point.

    b^2 - 4(1)(1) = 0
    b = 2 or -2

    So now you know that x^2 +/-2x +1 has one real root.

    Also x^2 + 5x +2 = x^2 +/-2x +1 + mx + 1
    (This is from the beginning, where you had 4x+1=x^2 + 5x +2 and you subtracted 4x+1 from both sides. You know you want x^2 + 5x +2 - 4x +1 to equal x^2 +/-2x +1 (for in this instance there is one root), so Also x^2 + 5x +2 = x^2 +/-2x +1 + mx + 1)

    Therefore m = 7 or 3
    where are you getting the b=2 or -2 from
    b=1 therefore 1^2 =1
    so 1-4 = -3?
  17. Offline

    ReputationRep:
    (Original post by Mr M)
    I think you need to speak to your teacher now hamzah. We can teach you a mechanical process but, with absolutely no understanding, there is little chance you will ever be able to apply it.
    i dont understand how we do similar stuff in class which i understtand but for homework i dont understand it
    arrghh
  18. Offline

    ReputationRep:
    (Original post by hamzah190)
    where are you getting the b=2 or -2 from
    b=1 therefore 1^2 =1
    so 1-4 = -3?
    I've edited my post to show more working.
  19. Offline

    ReputationRep:
    (Original post by hamzah190)
    i dont understand how we do similar stuff in class which i understtand but for homework i dont understand it
    arrghh
    See your teacher - ask him or her to make sure you understand how the discriminant can be used to find out information about the intersection of lines and curves.
  20. Offline

    ReputationRep:
    (Original post by hamzah190)
    where are you getting the b=2 or -2 from
    b=1 therefore 1^2 =1
    so 1-4 = -3?
    still dont understand mate

    how did you get b^2 -4 (1)(1) = to -2 or +2

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: October 16, 2011
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

New on TSR

Improving your uni offer

Why now is the time to think about Adjustment

Study resources
x

Think you'll be in clearing or adjustment?

Hear direct from unis that want to talk to you

Get email alerts for university course places that match your subjects and grades. Just let us know what you're studying.

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