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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.
What else can I help you with?
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.
How do you find solutions of equations?
To find solutions of equations, you can use various methods depending on the type of equation. For linear equations, you can isolate the variable by performing algebraic operations. For polynomial equations, techniques like factoring, using the quadratic formula, or graphing may be employed. For more complex equations, numerical methods or software tools can be helpful in approximating solutions.
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 do these applications of quadratic equations and function affect you?
It would help if there was a little bit more information about "these".
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.
How do you find solutions of equations?
To find solutions of equations, you can use various methods depending on the type of equation. For linear equations, you can isolate the variable by performing algebraic operations. For polynomial equations, techniques like factoring, using the quadratic formula, or graphing may be employed. For more complex equations, numerical methods or software tools can be helpful in approximating solutions.
What is a equation with an equal sign called?
An equation with an equal sign is called an "equation." It represents a mathematical statement that asserts the equality of two expressions. Equations often involve variables and can be solved to find the values that make the statement true. Examples include linear equations, quadratic equations, and more.
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.
