In reality most people are not going to use the quadratic equation in daily life. Having a firm understanding of the quadratic equation as with most math, helps increase logical thinking, critical thinking, and number sense. So is the quadratic formula specific to the average person's life -- no. Could understanding the quadratic forumla help make you a more intelligent, rational individual -- yes. == == Imagine Bob, a shopkeeper, has a (square) tray of apples. While carrying the tray he trips and drops the apples all over the floor. His assistant comes out of the store room with a stack of 4 more trays. Clumsily he knocks the edge of the stack and a row of apples from each of the trays falls to the floor. Given that the total number of apples on the floor is 77 how many apples were on each tray to start?
The answer to this involves solving a quadratic equation, and is clearly very useful to Bob! That's cute! However, if Bob didn't already know that there were 49 apples on each tray, he is not much of a store manager and not very likely to understand the meaning of:
(a + 11)(a - 7) = 0
It's much faster in most cases; however, factoring is not always possible.
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:
There are several ways to solve such equations: (1) Write the equation in the form polynomial = 0, and solve the left part (where I wrote "polynomial"). (2) Completing the square. (3) Use the quadratic formula. Method (3) is by far the most flexible, but in special cases methods (1) and (2) are faster to solve.
signs or billboards
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. However, assuming your question to find the roots or solutions of ax2 + bx + c = 0, the answer is x = [-b ± sqrt(b2 - 4ac)]/2a b2 - 4ac is called the discriminant. If the discriminant > 0 then the quadratic equation has two distinct real roots. If the discriminant = 0 then the quadratic equation has one double root. If the discriminant < 0 then the quadratic equation has two distinct complex roots that are conjugates of one another.
in most engineering jobs
The quadratic formula is famous mainly because it allows you to find the root of any quadratic polynomial, whether the roots are real or complex. The quadratic formula has widespread applications in different fields of math, as well as physics.
It's much faster in most cases; however, factoring is not always possible.
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.
The most common source of fluoride in daily life is toothpaste.
Most likely referring to glucose
Use the quadratic formula. A calculator will help with the squares and fractions and especially with square roots. If the equation is ax2 +bx +c = 0, then x = (-b +/- sqrt(b2-4ac))/2a. With a simple equation like x2+5x-6=0, you can solve by factoring: (x+6)(x-1)=0 <=> x=-6 or x=1. However, the quadratic formula will work on any equation.
The most surefire way to find the zeroes of a quadratic are to apply the quadratic formula. The formula says that the zeroes of quadratic equations which are generally written as ax2+bx+c=y can be found by taking (-b+/-(b2-4ac).5)/2a or if this notation makes no sense... negative b plus or minus the square-root of b squared minus four ac all over two a. Note: if b squared minus four ac is less than zero, the function has non-real roots
two solutions
Two solutions
MnO2 is the most common version