The solution set is the set of all points representing solutions.
No. They can just as well have zero solutions, several solutions, or even infinitely many solutions.
It depends on the polynomial and your degree of sophistication. In the complex domain, it will have six solutions, although not all of them need be different. If the coefficients are all real, then it will have 0, 2, 4 or 6 real solutions in the real domain.
You may be able to give a formula that represents all the solutions. For example, the equation sin(x) = 0 where x is real, has infinitely many solutions but they can be summarised, very simply, as x = n*pi radians (180*n degrees) where n is any integer. Some solution sets are harder to summarise.You may be able to give a formula that represents all the solutions. For example, the equation sin(x) = 0 where x is real, has infinitely many solutions but they can be summarised, very simply, as x = n*pi radians (180*n degrees) where n is any integer. Some solution sets are harder to summarise.You may be able to give a formula that represents all the solutions. For example, the equation sin(x) = 0 where x is real, has infinitely many solutions but they can be summarised, very simply, as x = n*pi radians (180*n degrees) where n is any integer. Some solution sets are harder to summarise.You may be able to give a formula that represents all the solutions. For example, the equation sin(x) = 0 where x is real, has infinitely many solutions but they can be summarised, very simply, as x = n*pi radians (180*n degrees) where n is any integer. Some solution sets are harder to summarise.
No. Some have two solutions where as some have none.
yes it is a solution, and all solutions are mixtures, but all mixtures are not solutions.
(Disregarding gases) All solutions are liquids but not all liquids are solutions.
(Disregarding gases) All solutions are liquids but not all liquids are solutions.
The solution set is the set of all points representing solutions.
Not necessarily. A solution is a kind of mixture but not all mixtures are solutions.
The formula you are recalling is called the quadratic equation, but you have it slightly mistated. The correct statement is... For a polynomial of degree two, in the form Ax2 + Bx + C = 0, the solution for x is... (-B ± square root (B2 - 4AC)) / 2A The discriminant, B2 - 4AC, identifies the number and type of solutions. If it is zero, there is one real solution. If it is positive, there are two real solutions. If it is negative, there are two complex conjugate (real, imaginary) solutions.
Yes, all solutions are by definition mixtures.
No, not all solutions are liquids. Solutions can be liquids, gases, or solids. For example, air (a gas solution of oxygen, nitrogen, and other gases) and brass (a solid solution of copper and zinc) are both examples of solutions that are not in liquid form.
Yes, all solutions are by definition mixtures.
Yes, all solutions are by definition mixtures.
There are infinitely many ordered pairs tat are solutions. They are all points on the line represented by 5x-6y = 13
Because 8 does not = 7, there is no solution. You write No Sol. Alternatively if you simplify an equation to x = x, that would be All Solutions (any number substituted for x satisfies the equation) * * * * * Wrong! 8x = 7x DOES have a solution and that is x = 0