Question

Would someone please explain how should I solve this? The line y=mx intersects the curve at y=1/4(x^3-6x^2+8x) at three points. Find the least possible value of m.
-Graph attached.

Answer 1

4y= 4mx =x^3 - 6x^2 + 8x
=>x(x^2 -6x +8-4m) =0
1 soln is x=0
for the given quad eqn to have 2 solns,, b^2 -4ac >0
thus 36 - 4(8-4m)>0
find m> ?
which should be your ans.

Answer 2

HAHA. Genius. :D But I seriously didnot understand the purpose of using all these formulas.
Can you please explain in simpler terms?

Answer 3

what formullas ? b^2 - 4ac one ?

Answer 4

and its nothing like genius,,i just happened to be able to solve//its a rare occasion for me! ;)

Answer 5

No, seriously. That is pure genius! Yes, I didnot understand the logic behind it all. What I was doing was simply placing a ruler on the graph to find the point through which when y=mx passes, it will only cut through two points on the curve. O.o

Answer 6

hmmn,,do you know about the quadratic formulla ?

Answer 7

Yes, I do know about that. But why apply it here? O.o

Answer 8

theres a discriminant in there D = b^2 - 4ac
the roots depend on it as it is under a sqrt.
is b^-4ac > 0,,the sqrt will give out some real value and the eqn will have 2 solns
if its =0,,eqn will have 1 real root,,if its <0,,the sqrt doesnt exist in real world and theres a complex solution to it
your ques req it to have 2 more intersections besides at 0..
so we had to it >0
again i'll ask,,was i clear enough? ;)

Answer 9

Oh! Now I get it. Thank you so much for helping and being patient.

Answer 10

hmmn,,and i'll say again,,glad to have helped! ^_^