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# f(x) = x^3 - 4x^2 - 3x + 25 has no rational roots.  Use the graphing calculator to...

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f(x) = x^3 - 4x^2 - 3x + 25 has no rational roots.  Use the graphing calculator to approximate the irrational solutions correct to 3 decimals.

If there is more than 1 Real solution, enter from smallest to largest.

Posted by kristenmariebieber on July 29, 2013 at 2:01 AM via web and tagged with algebra2, math

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Given `f(x)=x^3-4x^2-3x+25` we are asked to find the real roots.

This is a cubic with a positive leading coefficient. The graph will rise as x goes from negative to positive. The graph can have at most 2 turning points (points where the graph changes from increasing to decreasing or vice versa.)

Graph using technology:

There is only 1 x-intercept, and thus 1 real root. The root is located between -3 and -2. Using a graphing utility we find the approximation for the root to be -2.253619

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To 3 decimal places the required root is `x=-2.254`

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Posted by embizze on July 29, 2013 at 2:17 AM (Answer #1)