# Math: Polynomial inequalities

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solve the Math: Polynomial inequality and express the solution in set notation.

2t^2 - 3 < or = to t

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1. Inequalities involving parabolas can get interesting.

Solve as an equation:

2t^2 - t -3 = 0
(t+1)(2t-3) = 0
t = -1 or 3/2

Think now of the graphs of 2t^2 - 3 and t

You want the region where the parabola is below the line. That is,

-1 <= x <= 3/2

Of course, you can do analysis of the factors, considering positive and negative values, but it's a lot more work, and gets you the same result.

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