If 2 + 3 i is one of the roots of the equation 2 x 3 - 9 x 2 + k x - 13 = 0 , k ∈ R , then the real root of this equation (where i 2 = - 1 ) :

Step-by-step solution

If 2 + 3 i in one of the roots, then 2 - 3 i would be other. Since coefficients of the equation are real. Let γ be the third root, then product of roots →     α   β   γ   = 13 2 2 + 3 i   2 - 3 i   ⋅ γ = 13 2   4 + 9 ⋅ γ = 13 2 ⇒ γ = 1 2 The value of k will come if we put x = 1 2 in the equation 2 ⋅ 1 8 - 9 4 + k ⋅ 1 2 - 13 = 0 ⇒ k 2 = 15 ⇒ k = 30 ∴     Equation will become 2 x