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The equation must be written such that the right side is equal to zero. And the resulting equation must be a polynomial of degree 2.

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0"The coefficient of the x^2 term must be positive" is a condition that does not have to be met.

If the discriminant of the quadratic equation is less than zero then it has no real solutions

That the discriminant of the quadratic equation must be greater or equal to zero for it to have solutions. If the discriminant is less than zero then the quadratic equation will have no solutions.

The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.

the formula you are going to use to answer the equation

Only that the equation that you are trying to solve is a quadratic, that is to say, the powers of the variable are 2,1 and 0 (or any constant increment of these three numbers). Non-negativity of the discriminant is NOT a condition because you can still use the quadratic formula and get roots that are in the complex domain.

subtract

Somebody (possibly in seventh-century India) was solving a lot of quadratic equations by completing the square. At some point, he noticed that he was always doing the exact same steps in the exact same order for every equation. Taking advantage of the one of the great powers and benefits of algebra (namely, the ability to deal with abstractions, rather than having to muck about with the numbers every single time), he made a formula out of what he'd been doing:The Quadratic Formula: For ax2 + bx + c = 0, the value of x is given byThe nice thing about the Quadratic Formula is that the Quadratic Formula always works. There are some quadratics (most of them, actually) that you can't solve by factoring. But the Quadratic Formula will always spit out an answer, whether the quadratic was factorable or not.I have a lesson on the Quadratic Formula, which gives examples and shows the connection between the discriminant (the stuff inside the square root), the number and type of solutions of the quadratic equation, and the graph of the related parabola. So I'll just do one example here. If you need further instruction, study the lesson at the above hyperlink.Let's try that last problem from the previous section again, but this time we'll use the Quadratic Formula:Use the Quadratic Formula to solve x2 - 4x - 8 = 0.Looking at the coefficients, I see that a = 1, b = -4, and c = -8. I'll plug them into the Formula, and simplify. I should get the same answer as before:

Police, Quadratics, Action! If you know the initial speed of car, how far you are travelling and what your acceleration is, there is a special formula that lets you find out how long the journey will take. This formula is a quadratic with time as its unknown quadratic quantity. The police use this equation - along with many other quadratic and non-quadratic equations - when they attend a road traffic accident (RTA). They do this to find out if the driver was breaking the speed limit or driving without due care and attention. They can discover how fast the car was going at the time the driver started braking and how long they were braking for before they had the accident. This is done by finding the road's coefficient of friction and by measuring the length of the skid marks of the vehicles involved. Once they have this information they turn to Mathematics and the trusted quadratic equation. Einstein's Famous Quadratic The most famous equation in the world is technically quadratic. Einstein discovered the formula: Where E is the Energy of an object, m is its mass and c is the speed of light. This formula relates mass and energy and came from Einstein's work on Special and General Relativity. However, in practice it is not solved as a quadratic equation as we know the value of the speed of light. For more information on Einstein and his Theory of Special Relativity see the links at the bottom of the page. There are many more uses for quadratic equations. For more information please see the links to "101 Uses of a Quadratic Equation" at the bottom of the page.

There are a number of different ways. The one way which always works is using the quadratic formula.So, the solutions of quadratic equation of the form ax2 + bx + c = 0 arex = [-b Â± sqrt(b2 - 4ac)]/(2a)If b2 - 4ac, which is called the discriminant, is less than 0 then there is no real square root and so no real solution: if a > 0 the graph of the quadratic is either entirely above the x-axis and if a There are other methods such as completing the square which is, in fact, the same as the above but you go through a lot more steps before getting to the same point!Still another method is factorisation. This method is fine as long as you can easily work out two linear factors for the quadratic. A lot of high school quadratics that you will need to solve will be open to this approach but real life is not as simple!

Vertices in quadratic equations can be used to determine the highest price to sell a product before losing money again.

you need a quadratic equation for this ½ at2 + vot - s = 0 vertical acceleration (a) is gravity (-9.8ms-2) initial vertical velocity is 0 his vertical height above ground is 200 (s=200) pop all that in the equation and you're done yep... and I'm sorry but I've had to delete my quadratic formula off my calculator and I've finished maths for the year and can't be stuffed doing it by hand.. you know the quadratic formula.. have fun :)

Sure, you can (a = 9, b = 0, c = -144). However, in this case, since there is no linear term, it is easier to transfer the -144 to the right (9x2 = 144), then take the square root on both sides. Don't forget to add "plus or minus" before one of the terms, or you will miss one of the two solutions.

This is the generalized trinomial equation (aka quadratic):y = ax2 - bx - cBefore factoring, always check the discriminant of the quadratic equation, which is:b2 - 4acIf it is a rational square (16, 25, 196, 225), then it is factorable. If it is not, then it is not factorable.In this case, it is not, since the discriminant is equal to 2âˆš3.Now, you will have to use the quadratic formula:(-b2 +/- âˆš(b2 - 4ac))/2This will give you (14 +/- 2âˆš3)/2

David did not measure the solutions' volumes before mixing the solutions.

Before a symbol. Not sure about a formula.

why the need for unification in both India & GermanyAnswercondition of Germany before 1871 Answercondition of Germany before 1871 Answercondition of Germany before 1871 AnswerCondition OF India immediately after 1947

The expression is faulty because we don't have + or - before 10a. Also have to assume a2 is a2 . Use the standard formula for solving a quadratic = 0, to get two answers p and q. Then the factorization is (a-p)(a-q).

very bad condition

You must understand rudimentary math before you tackle quadratic equations. (rudimentary = basic)

The purpose is to avoid splashing.

Most of the solutions before the Final Solution were not killing. The Jewish question was what to do with the Jews, they had tried to get them to emigrate, they had tried to deport them, to slowly starve them, there were more suggested solutions, like sterilization, but the Final Solution was to outright murder them.

Distilled water is recommended to be boiled and cooled before preparing NaOH solutions to eliminate the dissolved CO2 in the distilled water.

This is number before the chemical formula.

Sure if you had been treated or had symptoms of arthritis before taking out whatever you are talking about then it would be a pre-existing condition. Anything that existed before is a pre-existing condition.

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