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sir if x^3-31x+30=0 then how we will find values of x



if x^3-31x+30=0

then how we will find values of x


1 Answers

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
11 years ago

Dear Sunil Sahu,

Solution:- General approach for solving the cubic equation is to first find one root (say 'a') by Hit and Trial method. Then, you will break the equation into two parts like  (x-a)(x^2 - bx + c) = 0.

After this step, you know the one root and you get one quadratic equation (in above case, it is x^2 - bx + c = 0). Solve the quadratic equation and get another two roots.

For example (applying this method to your problem),

(1) x^3 - 31x +30 = 0

Putting x=1 in the equation.

1 - 31 +30 = 0 which is true, which implies x = 1 is one of the root.

In most of the cases, putting 1,2,0,-1,-2,1/2 or -1/2 works.

(2) x^3 - 31x +30 = 0 can also be written as (x-1)(x^2 + x - 30) = 0

(3) Now solve the equation- x^2 + x - 30 = 0

It gives x = 5 and -6

Ans- x=1, 5 and -6

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All the best Sunil Sahu!!!



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Priyansh Bajaj

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