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    I did part a), but I fail to understand the rest of it. Could someone clear this out for me? I know that 'equal roots' implies that the discriminant is involved in solving the problem and b^2 - 4ac = 0. The curve will touch the x-axis, but how does that help me in finding k?
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    (Original post by frostyy)
    I did part a), but I fail to understand the rest of it. Could someone clear this out for me? I know that 'equal roots' implies that the discriminant is involved in solving the problem and b^2 - 4ac = 0. The curve will touch the x-axis, but how does that help me in finding k?
    The discriminant is b^2 - 4ac = (8k)^2 - 4(1)(k) = 0.
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    I understand that, but I'd like to know the logic behind that helping me to find k.
    And how would I solve it? Set 64k^2 - 4k = 0 and then just simply get k?

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    (Original post by frostyy)
    I understand that, but I'd like to know the logic behind that helping me to find k.
    And how would I solve it? Set 64k^2 - 4k = 0 and then just simply get k?

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    It gets you an equation in k, which you can then solve for k.

    Yep, k(64k - 4k) = 0 and you know that k \neq 0.
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    The fact that the discriminant = 0 means that the line is a tangent to the curve at the point of intersection.
    I want to clarify that because the discriminant = 0 that does not mean that the original curve will touch the x axis as you incorreclty said in your post.
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    But, at the same time, it does mean that the curve x^2 + 8kx + k does touch the x-axis.
 
 
 
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