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Other than the Quadratic Formula, there are two ways to solve a quadratic with a coefficient of more than 1 in the x2 term.
First, you can divide all terms by a common multiple if they have one, e.g.
2x2 + 10x + 12 can be divided by 2 to get x2 + 5x + 6, which factorises easily. If this doesn't work, then it's fine to skip straight to harder factorising.
First, multiply the final term by the coefficient of the x2 term.
e.g. for 3x2 + 4x - 7, multiply the -7 by the 3 to get -21.
Next, find which two numbers will multiply to get -21 and add to get 4, in this case 7 and -3.
Then, arrange the equation like this: (3x2 -3x) + (7x -7) , with the x coefficients matching up to the easiest number to divide by (this equation is easy, 3 matches with -3 and 7 matches with -7).
Factorise: 3x(x-1) +7(x-1)
Simplify: (3x+7)(x-1) Complete. Hope this helps.
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Is it possible for a quadratic equation to have more than 2 solutions?
No because quadratic equations only have 2 X-Intercepts
Equations 6-4x-3x² equals 0?
This is a quadratic equation requiring the values of x to be found. Rearrange the equation in the form of: -3x2-4x+6 = 0 Use the quadratic equation formula to factorise the equation: (-3x+2.69041576)(x+2.23013857) Therefore the values of x are 0.8968052533 or - 2.230138587 An even more accurate answer can be found by using surds instead of decimals.
Why Do you Study linear equations?
we study linear equation in other to know more about quadratic equation
How can apply quadratic equations in your life?
It really depends what you work in; if you work in science, or in engineering (applied science), you will need the quadratic equation - and a lot more advanced math as well. Examples that involve the quadratic equation are found in abundance in algebra textbooks; for example, an object in free fall.
Why is it better to solve quadratic equations in the complex number system rather than in the real number system?
It is not always better.Although quadratic equations always have solutions in the complex system, complex solutions might not always make any sense. In such circumstances, sticking to the real number system makes more sense that trying to evaluate an impossible solution in the complex field.
Is it possible for a quadratic equation to have more than 2 solutions?
No because quadratic equations only have 2 X-Intercepts
Equations 6-4x-3x² equals 0?
This is a quadratic equation requiring the values of x to be found. Rearrange the equation in the form of: -3x2-4x+6 = 0 Use the quadratic equation formula to factorise the equation: (-3x+2.69041576)(x+2.23013857) Therefore the values of x are 0.8968052533 or - 2.230138587 An even more accurate answer can be found by using surds instead of decimals.
How do these applications of quadratic equations and function affect you?
It would help if there was a little bit more information about "these".
Why Do you Study linear equations?
we study linear equation in other to know more about quadratic equation
Why are there usually two solutions to a quadratic equation?
In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.
How can apply quadratic equations in your life?
It really depends what you work in; if you work in science, or in engineering (applied science), you will need the quadratic equation - and a lot more advanced math as well. Examples that involve the quadratic equation are found in abundance in algebra textbooks; for example, an object in free fall.
Why is it better to solve quadratic equations in the complex number system rather than in the real number system?
It is not always better.Although quadratic equations always have solutions in the complex system, complex solutions might not always make any sense. In such circumstances, sticking to the real number system makes more sense that trying to evaluate an impossible solution in the complex field.
What are the applications of quadratic equations in every day life?
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.
What is the difference between a polynomial and a quadratic equation?
Oh, dude, it's like this: all quadratic equations are polynomials, but not all polynomials are quadratic equations. A quadratic equation is a specific type of polynomial that has a degree of 2, meaning it has a highest power of x^2. So, like, all squares are rectangles, but not all rectangles are squares, you know what I mean?
What are quadratic functions used for in everyday life?
Anything involving a square law automatically invokes a quadratic function by definition, even if the equations is as simple as y = x^2, such as the area of a square (hence the names). At a more advanced level, quadratic and higher-order functions crop up in all manner of real-life science and engineering problems.
Quadratic function in daily life?
Why Do We Study Quadratic Equation?In maths class, we are hammered with expressions after expressions of quadratic equations. We are taught how to solve for its roots. We are taught all the necessary methods or mathematical techniques to handle quadratic equations. But after all these, what is the purpose?This is the question many students of maths studies ask.Do we need this "quadratic" knowledge in working life?The communication dish is parabolic in shape. Parabolic is the equivalent to quadratic mathematically. Engineers need to understand quadratic equation to design this beautiful profile.the pan is a wok that is designed using quadratic expression. With this, food can be fried to our liking!Without quadratic equation, who knows how a wok would look like.eye-glass lens are constructed with curves matching that of the quadratic equation.Light is thus controlled to give good image to our eyes.Quadratic equations to the rescue, right?Other examplesare:1) Distance travelled given by the quadratic equation s = ut + (1/2) a t22) Electrical characteristics of a MOSFET (Transistor device)i = k [(Vg - Vt)VD - (1/2)Vd2]So now do you still wonder why you study quadratic equations?with out math these things wouldn't have existed then their would be no dish that will connect us to channels all over the world or like food how can we eat without a pan or even lenses, we all study math for a purpose and it's not just to pass an exam, it's to know more knowledge about whats around us
What is a quadratic eqation?
A quadratic equation is an equation where the highest exponent on the variable is 2. For example, the equation, y=2x2+3x-2 is a quadratic equation. The equation y=2x is not quadratic because the highest exponent on x is 1. (If there is no exponent on an x, then the exponent is 1.) The equation, y=x3+3x2-2 is not quadratic because the highest exponent is three. On a graph, a quadratic equation looks like a U or and upside down U. Here are some more example of quadratic equations: y=x2 y=3x2+2x-3 y=x2+5
