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Can i have some help on discriminants c1

I've become completely stuck on this question and seeing as how my teacher has been missing for 4 weeks i can't answer it. If you could help it would be gladly appreciated.

The curve C has equation y=4x-10x-x^2 and the line l has equation y=k(4x-12), where k is a constant.

i) Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the equation
x^2+2(2k+5)x-(13k+4)=0

ii) given that the curve c and the line l intersect at two distinct points show that
4k^2+33k+29>0

iii) solve the inequality 4k^2+33k+29>0


I've so far gotten i) down to 4-10x-x^2=k(4x-13) however i have no idea how to get rid of the k.
Reply 1
Avatar for davros
davros
16
Original post by randomhobo
I've become completely stuck on this question and seeing as how my teacher has been missing for 4 weeks i can't answer it. If you could help it would be gladly appreciated.

The curve C has equation y=4x-10x-x^2 and the line l has equation y=k(4x-12), where k is a constant.

i) Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the equation
x^2+2(2k+5)x-(13k+4)=0

ii) given that the curve c and the line l intersect at two distinct points show that
4k^2+33k+29>0

iii) solve the inequality 4k^2+33k+29>0


I've so far gotten i) down to 4-10x-x^2=k(4x-13) however i have no idea how to get rid of the k.


Why do you want to "get rid of the k"? What you've written looks like a rearrangement of the answer they want - just try moving some terms over to one side!
Original post by randomhobo
I've become completely stuck on this question and seeing as how my teacher has been missing for 4 weeks i can't answer it. If you could help it would be gladly appreciated.

The curve C has equation y=4x-10x-x^2 and the line l has equation y=k(4x-12), where k is a constant.

i) Show that the x-coordinates of any points of intersection of the curve C with the line L satisfy the equation
x^2+2(2k+5)x-(13k+4)=0

ii) given that the curve c and the line l intersect at two distinct points show that
4k^2+33k+29>0

iii) solve the inequality 4k^2+33k+29>0


I've so far gotten i) down to 4-10x-x^2=k(4x-13) however i have no idea how to get rid of the k.

You know that the discriminant is b2−4acb^2-4ac
Solve k from the given quadratic. Then substitute into the equation you've given:
4−10x−x2=k(4x−13)4-10x-x^2=k(4x-13)
Reply 3
Avatar for TheManor
TheManor
6
to answer part (1) you don't have to get rid of the k - you just have to multiply your brackets out and then re-arrange
terms to get the answer

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