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the formula you are going to use to answer the equation

Q: What must be true of an equation before you can use the quadratic formula to find the solutions?

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Zero is an acceptable value for a variable. As a general rule, if you solve an equation and get x equals zero, that's just what it is: zero. There is one solution. Example: 10x +1 = 5x +1 5x = 1 - 1 5x = 0 x = 0 There is one solution, zero. If you solve for x and get two solutions, such as 2 and 0, there are two answers. Later on, if you've studied domain and range (the numbers you can use for x so that the equation is still defined, (i.e. not 1/0, or the square root of negative 1), you may find that x = 0 does not always work. You need to check first, to see if zero is in the domain, before you say it's an answer.

I believe the questioner means e^(-x^2), which is perhaps the most famous of many functions which do not have anti-derivatives which can be expressed by elementary functions. The definite integral from minus infinity to plus infinity, however, is known: It is sqrt(pi). The antiderivative to e^(-2x) is, (-*e^(-2x)/2) Though the anti-derivative (integral) of many functions cannot be expressed in elementary forms, a variety of functions exist only as solutions to certain "unsolvable" integrals. the equation erf(x), also known as the error function, equals (2/sqrt(pi))*integral e(-t^2) dt from 0 to x. As mentioned before, this cannot be expressed through basic mathematical functions, but it can be expressed as an infinite series. If the question is the antiderivative of e - x2, the answer is e*x - x3/3

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Contributions:Â· At 24 years of age, he wrote a book called Disquisitines Arithmeticae, which is regarded today as one of the most influential books written in math.Â· He also wrote the first modern book on number theory, and proved the law of quadratic reciprocity.Â· In 1801, Gauss discovered and developed the method of least squares fitting, 10 years before Legendre, unfortunately, he didn't publish it.Â· Gauss proved that every number is the sum of at most three triangular numbers and developed the algebra of congruences.Famous Quote:'Ask her to wait a moment - I am almost done.' Apparently said while working, and being informed that his wife was dying.

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The equation must be written in the form ( ax^2 + bx + c = 0 ), where ( a \neq 0 ). This is the standard form of a quadratic equation. If the equation is not in this form, you may need to rearrange it before applying the quadratic formula.

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.

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

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.

subtract

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

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.

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.

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 :)

from the equation using the formula -b/2a to find x value. from there substitute values of x before and after in equation.for example if x is 2 use other x values as 1 and 3.