Determine upper and lower bounds for the real roots of the equation. 5x⁴ - 10x - 12 = 0 A) 2 is an upper bound, - 1 is a lower bound B) 8 is an upper bound, - 1 is a lower bound C) 1 is an upper bound, - 2 is a lower bound D) 2 is an upper bound, - 4 is a lower bound E) 8 is an upper bound, - 4 is a lower bound

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Quizplus · Accepted Answer

The Descartes' Rule of Signs can be used to determine the upper and lower bounds for the real roots of the given polynomial equation. The equation given is $5x^4 - 10x - 12 = 0$. By applying the rule of signs to the polynomial and its derivative, we can infer that 2 is an upper bound because substituting any value greater than 2 into the polynomial results in positive values, indicating no sign changes and thus no roots beyond this point. Similarly, -1 can be considered a lower bound because substituting any value less than -1 results in a consistent sign, indicating no roots beyond this point.

Determine Upper and Lower Bounds for the Real Roots of the Equation