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# Cubic Equations

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 Sub Topics The polynomials can be of the following types: linear polynomial, quadratic polynomial and the cubic Polynomials. If we talk about the Cubic Equations, we say that the standard form of the cubic Equation is ax3 + b.x2 + cx + d = 0, where we have a, b, c and d as the real Numbers and a <> 0. Now we look at the Cubic Equations and the method of solving the Cubic Equations. The Cubic Equations can be solved by finding the common factor of the given equation and then dividing the given equation by the common factor. In case the resultant factor i.e. the quotient is the quadratic polynomial, then we say that the solution of this can be done by any of the methods of solving the quadratic equations. Here we will observe the relation between the zeros and the coefficients of cubic equations. Let α, β, γ are the three zeroes of the given cubic polynomial. We know that the cubic equation can have maximum of three zeroes. So if we have p(x) = ax3 + b.x2 + cx + d, where a < > 0, then we say that (x-α ) ,( x - β) ,( x – γ) are the factors of p(x). So we have ax3 + b.x2 + cx + d = k. (x - α) * (x - β) * (x – γ) for some constant ‘k’. On comparing we get k = a, -k * (α + β + γ) = b, k * (α* β + β* γ + γ * α) = c and -k (α* β* γ) = d. Putting the value of k = a, we get (α + β + γ) = b/ a, (α* β + β* γ + γ * α) = c/a and α* β* γ = - d/ a.