Two of the roots of the equation 2x^3-5x+1=0 lie in the intervals?

Question

I can't solve this equation, can anyone help me?

Answer 1

The cubic function is 2x³ - 5x + 1 = 0

Graph

 

The points where it crosses the x  axis  will give solutions to the polynimial function .

The graph crosses the x  - axis at a point that would suggest a factor.

It crosses the x  - axis at one point hence there are three real roots.

x  =1.48

Use synthatic division to detrmine if the given value of x  is a root of the polynomial.

Since f (1.48) = 0, x = 1.48 is a zero.

The depressed polynomial is

Use the Quadratic Formula to find the roots of the related quadratic equation

 

Roots are

Solutions of the cubic function.

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The three roots of the cubic function lies between the interval (-2,2).