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=2x=-2 value of the function=3×(2)213×(2)+10=48=3\times(-2)^2-13\times(-2)+10=48

And at x=2x=2 value of the function=3×2213×2+10=(4)=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 XaxisX-axis at least once.

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


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