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

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

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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?
Reply 2
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?
Actually, it has to be 0.:smile:
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.
Reply 5
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 ?
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?
Reply 7
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)
Reply 8
Original post by hamzah190
b^2 -4ac

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


yes
Reply 9
Original post by TenOfThem
yes


so i got 1^2 -4(1)(1)

which is -3

what do i do now
Reply 10
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.
Reply 11
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
Reply 12
What you need to do is set b^2-4ac = 0, then solve to find those values, using your previous equations.
Reply 13
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
(edited 12 years ago)
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.
Reply 15
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?
Reply 16
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
Reply 17
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.
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.
Reply 19
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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