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# A-level C1, Simultaneous Equations with k Watch

1. Bit stuck here...

The question is 'Find the range of values of k for which kx + y = 3 meets x^2 + y^2 = 5 in two distinct points.

I've rearranged the first equation so that y = 3 - kx and then I substituted it in to the other equation.

x^2 + (3 - kx)(3-kx)
= x^2 - 6kx + k^2x^2 + 9

Would I use the discriminant now? I have trouble in trying to figure out a, b and c. I know that a = 1 but would the k^2x^2 be part of b or part of c?

Edit: The answer is supposed to be k < -2/5 root5 or k > 2/5 root5 but I'm confused as to how they get this.
2. Make the equation = 0 then use discriminant.

EDIT: take out common factor of x^2 to get (k^2 + 1) x^2 ; that is your a
3. (Original post by soup)
Make the equation = 0 then use discriminant.

EDIT: take out common factor of x^2 to get (k^2 + 1) x^2 ; that is your a
Okay, I've done this and put it into the discriminant but still getting wrong answers. Maybe I've made a mistake somewhere else?

I just get:
36k^2 - 36k^2 - 36 > 0
And it is impossible to get a positive answer like that...
4. (Original post by Deceiver)
Okay, I've done this and put it into the discriminant but still getting wrong answers. Maybe I've made a mistake somewhere else?

I just get:
36k^2 - 36k^2 - 36 > 0
And it is impossible to get a positive answer like that...
What's your a, b and c?
5. (Original post by soup)
What's your a, b and c?
Well if my equation is (k^2 + 1)x^2 - 6kx + 9 > 0 then a = k^2 + 1, b = -6 and c = 9, right?
6. (Original post by Deceiver)
Well if my equation is (k^2 + 1)x^2 - 6kx + 9 > 0 then a = k^2 + 1, b = -6 and c = 9, right?
b is -6k and you haven't rearranged the equation with x to equal 0 properly.

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