Question

The equation x^3-3x+a=0 will have exactly one root if

Answer 1

Answer:

If the equation x3−3x+a=0 has 3 distinct roots between 0 and 1 then the integer value of a is

Can we solve it without Calculus.

MyTry:: Let x=2cosϕ, where −1≤cosϕ≤1⇒0≤ϕ≤π(Principle value, Inverse exists)

8cos3ϕ−6cosϕ+a=0⇒4cos3ϕ−3cosϕ=−a2⇒cos3ϕ=−a2

Now −1≤cos3ϕ≤1, So −1≤−a2≤1⇒−2≤a≤2

So we get a={−2,−1,0,1,2}

But answer is no integer value of a

Thanks