Question

what are the roots of the equation
${x}^{3} + {x}^{2} - \: x \: + 2 = 0$
Dont dare to span other wise clear report.
Show every method this equation could be solved.​

Answer 1

Answer:



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Class 9

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>>Polynomials

>>Factorisation of Polynomial

>>The roots of the equation x^3 - 3x - 2 =

Question



The roots of the equation x3−3x−2=0 are

A

−1,−1,2

B

−1,1−2

C

−1,2,3

D

−1,−1,−2

solution

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+