Author Topic: Quadratics help  (Read 974 times)

Offline spiderman

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Quadratics help
« on: November 27, 2009, 02:09:18 pm »
Hey guys, pls cud any1 help me wit this question......

Find the set of values of k for which the line y=kx-4 intersects the curve y=x^2-2x at two distinct points??????
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Offline astarmathsandphysics

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Re: Quadratics help
« Reply #1 on: November 27, 2009, 02:38:36 pm »
When i get home.

Offline staceyboy3

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Re: Quadratics help
« Reply #2 on: November 27, 2009, 03:10:19 pm »
y=kx-4 and y=x^2-2x

intersects so kx-4=x^2-2x

simplify into the form: x^2 - (k+2)x + 4 = 0

when it comes to points of intersection, you look a the discriminant D=b^2-4ac, when ax^2+bx+c=0
intersects at 2 points so D > 0

(k+2)^2 - 4*1*4 > 0
k^2 + 4k -12 > 0

Change it to k^2 + 4k -12 = 0
and solve for k

k=2 or k=-6

Now you draw a graph (parabola shape of U on x-axis)
Looking back at k^2 + 4k -12 > 0, we want all the values that are above the x-axis (>0)

       |                  |
        \                /       +
          \            /
--------0------0---------->
        -6  \ _ _ / 2          -

That occurs when k<-6 or k>2

Hope the diagram isn't too confusing  :)
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Offline vanibharutham

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Re: Quadratics help
« Reply #3 on: November 27, 2009, 05:27:52 pm »
I do a different method

if this helps you here is how i do it:

y=kx-4 and y=x^2-2x

intersects so kx-4=x^2-2x

simplify into the form: x^2 - (k+2)x + 4 = 0

when it comes to points of intersection, you look a the discriminant D=b^2-4ac, when ax^2+bx+c=0
intersects at 2 points so D > 0

(k+2)^2 - 4*1*4 > 0
k^2 + 4k -12 > 0

Change it to k^2 + 4k -12 = 0
and solve for k

k=2 or k=-6



The same upto there :)

now, i draw a number line

<-------[-6]-----------------------[2]--------------->

To find out your range you pick values from the number line

lets say 0, and we plug this into our equation...

k² + 4k -12 > 0
(0) + (0) - 12 = - 12 which is NOT greater than zero

hence, we know that k can not lie between -6 and 2

so the only possibility is that

k < -6 and k > 2
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Offline spiderman

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Re: Quadratics help
« Reply #4 on: November 28, 2009, 03:52:47 am »
Thanks a lot guys!!!!! :)
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Offline staceyboy3

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Re: Quadratics help
« Reply #5 on: November 28, 2009, 09:05:55 am »
No problem  ;)
Relax, enjoy and be LAZY!