Answer to Question #95329 in Real Analysis for Rajni

Question

Examine whether the equation x^3- 13x +10 =0 has a real root in the interval ]-2,2[ ?

Answer 1

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 $[-2,2]$ .