Quadratic problem

[rongmon]

The number of points at which the equation y = x^6 + x^3 - 2 cuts the x axis is

a. 1

b. 2

c. 4

d. 6

I tried solving for first derivative which is positive, from which i gathered answer as a.

Answer stated as b., how does one check for this?

[Noel]

Put x^3=t so the equation becomes
t^2+t-2=0
solve this to get t=1 and t=(-2)
i.e. x^3=1 and (-2)
so x=1 and x=(-2)^(1/3)
hence option b

[rongmon]

Great.

Do you have any examples/ workings of integration of fractional functions - please share if you do.

[rongmon]

The number of real roots of the equation 8x^3 -6x +1 =0 lying between -1 and 1

a.0

b.1

c.2

d.3

[Dreyfus]

There is 1 real root...in (-1,-3/4)

[Mansigupta]

Can u please explain how to solve this question?