Question

show that the equation 6x^4-7x+1=0 does not have more than two distinct real roots ( use roll's theorem)

Answer 1

The graph of the equation wil be an upward parabola(or a curve similar to that)...
Firstly differentiate the equation..and put it equal to zero,,,u wil find a particular x...
which will be the critical point of the orignal curve(maxima or minima)..now putting this x back into the orignal equation,,you will find that the value is negative...which means some parabola lies below the x-axis(as the parabola is upward)..which can only happen if the parabola has cut the x-axis at two points..
so two roots,,which are real...now
since there there are no more critical points...so there are no more real roots...

Answer 2

thanks plz expain critical point easy definaton

Answer 3

well..u can understand critical points on a graph to be that points where the nature of the graph change..or simply(but not always)where the slope of the graph becomes zero...