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Help with this C1 question

Hey found this question on a C1 OCR MEI 2013 paper, can't figure out how to do this without using calculus by equating the two gradients or visually using the graph. How would you approach this using the discriminant as it shows in the mark scheme? Cheers
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Put them equal to each other to solve simultaneously then set this equal to 0 to form a quadratic. Now...

You know that if the line is a tangent to the curve, then they only 'touch' once i.e. a repeated root. This tells us that b^2 -4ac = 0 then solve this for k.
Original post by ericent
Hey found this question on a C1 OCR MEI 2013 paper, can't figure out how to do this without using calculus by equating the two gradients or visually using the graph. How would you approach this using the discriminant as it shows in the mark scheme? Cheers


Equate the two, get a quadratic, set the discriminant equal 0 for a single root (thus a single intersection -> tangent).
Reply 3
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ericent
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Thanks, but I've tried that, maybe my working is wrong but here it is:
Quadratic equation formed is: x^2-(k+2)x+2k+1
So a=1 b=-(k+2) c=2k+1
b^2-4ac=0
When substituted in, I get k^2+12k+8, obviously, here it can't be factorized without it being irrational and the mark scheme has 2 solutions for k, k=0 and k=4
Screen Shot 2017-05-16 at 14.14.47.png
Original post by ericent
Thanks, but I've tried that, maybe my working is wrong but here it is:
Quadratic equation formed is: x^2-(k+2)x+2k+1
So a=1 b=-(k+2) c=2k+1
b^2-4ac=0
When substituted in, I get k^2+12k+8


You expanded/simplified wrong at some point then.
Reply 5
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ericent
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1
Original post by RDKGames
You expanded/simplified wrong at some point then.
Oops looks like I had, got it now, thanks very much for the quick help!

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