The number of cubic equations that can be formed with the coefficients 0, 3, 2, 4, 5, 6 when repetition of coefficients is allowed, is....

Step-by-step solution

A cubic equation is of the form ax^3 + bx^2 + cx + d = 0 , where a 0 . The given set of coefficients is 0, 2, 3, 4, 5, 6 , which contains 6 elements. Since a 0 , the coefficient a can be chosen in 5 ways (any number from the set except 0). The coefficients b, c, and d can each be chosen in 6 ways, as repetition of coefficients is allowed. Total number of cubic equations = 5 6 6 6 = 1080 . Answer: 1080