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How does the discriminant relate to this?


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?
Reply 1
Avatar for Zacken
Zacken
22
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 b2−4ac=(8k)2−4(1)(k)=0b^2 - 4ac = (8k)^2 - 4(1)(k) = 0.
Reply 2
Avatar for frostyy
frostyy
OP
17
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?

Posted from TSR Mobile
Reply 3
Avatar for Zacken
Zacken
22
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?

Posted from TSR Mobile


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

Yep, k(64k−4k)=0k(64k - 4k) = 0 and you know that k≠0k \neq 0.
Reply 4
Avatar for B_9710
B_9710
18
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.
Reply 5
Avatar for Zacken
Zacken
22
But, at the same time, it does mean that the curve x2+8kx+kx^2 + 8kx + k does touch the x-axis.

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