What are the solutions of the equation x3 plus 3x2-x-3 equals 0?

Answer 1

the solutions to this equation are -1,+1 and -3.

you can solve this equation by using the polynomial long division method. we basically want to factorize this and polynomial and equate its factors to zero and obtain the roots of the equation. By hit and trial , it clear that x=1 i.e is a root of this equation. So (x-1) should be a factor of the given polynomial (LHS). Divide the polynomial by x-1 using long division method and you will get the quotient as x2+4x+3 and remainder would be 0 ( it should be 0 as we are dividing the polynomial with its factor. Eg when 8 is divided by any of its factor like 4,2 .. remainder is always zero )

Now, we can write the given polynomial as product of its factors as

x3+3x2-x-3 = (x-1)(x2+4x+3)

=(x-1)(x+1)(x+3) [by splitting middle term method]

so the solutions for the given polynomial are obtained when RHS = 0, Hence x=-1 , X = +1, x=-3 are the solutions for this equation.