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

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    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

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    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?
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    (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?
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    Actually, it has to be 0.
  5. Offline

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    (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

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    (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

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    (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

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    (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

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

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

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

    which is -3

    what do i do now
  11. Offline

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    (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

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    (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

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

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    (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
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    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

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    (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?
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    (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

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    (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

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    (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

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    (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

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