1. Calculate the greatest root of 2x^3-4x^2-3x+1=0, to three decimal places.Show all steps

See here: The Cubic Formula

Plug in your a=2, b=-4, c=-3, d=1 into that cumbersome formula.

Yes, there is a formula (like the quadratic formula) for cubics. It is rather large by comparison, but will work.

The fact that a decimal approxiation is required suggests that you're meant to use technology (graphics calculator, CAS, whatever you've been taught to use). Most likely, graph y = 2x^3-4x^2-3x+1 and use the technology to get the largest x-intercept.

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