Answer to Question #95329 in Real Analysis for Rajni

Question #95329
Examine whether the equation x^3- 13x +10 =0 has a real root in the interval ]-2,2[ ?
1
Expert's answer
2019-09-30T11:01:00-0400

At "x=-2" value of the function"=3\\times(-2)^2-13\\times(-2)+10=48"

And at "x=2" value of the function"=3\\times2^2-13\\times2+10=(-4)"

As the given function is a polynomial function which are continuous and value of the function changes from positive to negative, it must have cut the "X-axis" at least once.

Hence there exists a real root between "[-2,2]" .


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