Which way should i be answering this question?

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nicevans1
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#1
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Question

Find the range of values of M for which the line y=mx-5 intersects the curve y=x^2-4x+5 in two distinct points.

I completed the question by integrating the linear into the quadratic and then solved by working the discriminant.
I have the 2 answers as -6 and -2

I,m just unsure whether the range will be m>-6 & m<-2 or m<-6 & m>-2

Why, from the wording of the question should i or would i know whether they want the range of m below or above the x axis?


Thanks
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I_Like_Maths
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(Original post by nicevans1)
Question

Find the range of values of M for which the line y=mx-5 intersects the curve y=x^2-4x+5 in two distinct points.

I completed the question by integrating the linear into the quadratic and then solved by working the discriminant.
I have the 2 answers as -6 and -2

I,m just unsure whether the range will be m>-6 & m<-2 or m<-6 & m>-2

Why, from the wording of the question should i or would i know whether they want the range of m below or above the x axis?


Thanks
It might help if you draw graphs out like you normally would when solving quadratic inequalities. It should make it easier to see.
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TeeEm
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(Original post by nicevans1)
Question

Find the range of values of M for which the line y=mx-5 intersects the curve y=x^2-4x+5 in two distinct points.

I completed the question by integrating the linear into the quadratic and then solved by working the discriminant.
I have the 2 answers as -6 and -2

I,m just unsure whether the range will be m>-6 & m<-2 or m<-6 & m>-2

Why, from the wording of the question should i or would i know whether they want the range of m below or above the x axis?


Thanks
I cannot check your answer but if these 2 answers are correct look at your textbook "how to solve quadratic inequalities"
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TenOfThem
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(Original post by nicevans1)
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Wondering where you got the -6 and -2 from
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davros
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(Original post by nicevans1)
Question

Find the range of values of M for which the line y=mx-5 intersects the curve y=x^2-4x+5 in two distinct points.

I completed the question by integrating the linear into the quadratic and then solved by working the discriminant.
I have the 2 answers as -6 and -2

I,m just unsure whether the range will be m>-6 & m<-2 or m<-6 & m>-2

Why, from the wording of the question should i or would i know whether they want the range of m below or above the x axis?


Thanks
What did you get for the discriminant of your quadratic equation? I don't get anything involving -6 or -2 as solutions!
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nicevans1
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Sorry its y =x^2-4x+5 & y=mx+4 !!! I go the answers from the discriminant.


Regardles of the answer, what Im asking is - from the wording of the question why should i know if it wants the range to be above or below the x axis?


thanks
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davros
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(Original post by nicevans1)
Sorry its y =x^2-4x+5 & y=mx+4 !!! I go the answers from the discriminant.


Regardles of the answer, what Im asking is - from the wording of the question why should i know if it wants the range to be above or below the x axis?


thanks
You don't know from the wording of the question - that's the whole point!

All you know is that there must be two points of intersection, which requires the discriminant to be positive. Depending on what quadratic inequality comes out and how it factorizes will determine the appropriate range of values for m
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nicevans1
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Ok thanks Davros.

I just about come to that conclusion just before i read your answer. (honest)

It just confused the hell out of me because all though I knew the line intersects the curve at 2 points as it says in the question. The fact that we are trying to work out only the co-efficient of the linear equation y=mx+4 it just didn't register that the range of M would have to be above the x axis from a totally seperate quadratic equation

m^2-8m+12


Anyway I'm kind of there in my head.

Thanks

just for my reassurance if M was between -6 and -2 e.g below the x axis then the original y=mx+4 would NOT intersect x^2-4x+5
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james22
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(Original post by nicevans1)
Ok thanks Davros.

I just about come to that conclusion just before i read your answer. (honest)

It just confused the hell out of me because all though I knew the line intersects the curve at 2 points as it says in the question. The fact that we are trying to work out only the co-efficient of the linear equation y=mx+4 it just didn't register that the range of M would have to be above the x axis from a totally seperate quadratic equation

m^2-8m+12


Anyway I'm kind of there in my head.

Thanks

just for my reassurance if M was between -6 and -2 e.g below the x axis then the original y=mx+4 would NOT intersect x^2-4x+5
Your discriminant is inncorrect. How did you calculate it?

Also I'm not sure what you mean when you talk about being above or below the axis. Does you know how to solve quadratic inequalities?
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