question (1 Viewer)

[richz]

for wat values of m does the equation x^3 - 12x^2 + 45x - m = 0 have three distinct solutions?

thnx

 

[Ogden_Nash]

Let f(x) = x^3 - 12x^2 + 45x then find the stationary points of y = f(x). Then work out how far you can bring down the graph so that the stationary points are on opposite sides of the x-axis (ie 3 distinct roots). This will give you the values of m.

 

[Slidey]

That is:

x^3 - 12x^2 + 45x = m

m'=3x^2-24x+45=0
x^2-8x+15=0
x = 3, 5

m(3)=54
m(5)=50

Thus 51<=m<=53. If it were 50<=m<=54, you would be including when m gives only 2 roots (multiplicity).

 

[richz]

ok thnx thats what i got