Question

Find the number of real roots of the following equations. x ^3 – 3x + 2 = 0​

Answer 1

Step-by-step explanation:

x3−3x−2=0

Clearly x=−1 is a solution of the equation, hence (x+1) is a factor of the equation

        x2−x−2

        _______________

x+1)x3−3x−2

           x3   +x2

       __________________

                 −3x−2−x2

                −x      −x2

             ___________________

               −2x−2

               −2x−2

            ____________

                     0

            ____________

Now roots of the equation x2−x−2=0 will be roots of the given equation as well so,

⇒x2−x−2=0

⇒x2+2x−x−2=0

⇒x(x+2)−1(x+2)=0

⇒(x−1)(x+2)=0

Hence,

Factors ⇒(x+1)(x−1)(x+2)=0

Roots ⇒−1,1,−2.

Answer 2

Answer:

3 No of real roots of the following equation x³-3x+3=0

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