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Example:-
What are the dimensions of a rectangle when its length is greater than its width by 4 cm and has an area of 96 square cm?
Let the length be x+4 and the width x:
length*width = area
(x+4)*x = 96 => x2+4x-96 = 0 => (x+12)(x-8) = 0 when factored
So: x = -12 or x = 8 the dimensions can't be negative
Solution: length = 12 cm and width = 8 cm
Check: 12*8 = 96 square cm
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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.
What is the special cases of quadratic equation?
The standard form of a quadratic equation is: ax^2 + bx + c = 0. Depending on the values of the constants (a, b, and c), a quadratic equation may have 2 real roots, one double roots, or no real roots.There are many "special cases" of quadratic equations.1. When a = 1, the equation is in the form: x^2 + bx + c = 0. Solving it becomes solving a popular puzzle: find 2 numbers knowing their sum (-b) and their product (c). If you use the new Diagonal Sum Method (Amazon e-book 2010), solving is fast and simple.Example: Solve x^2 + 33x - 108 = 0.Solution. Roots have opposite signs. Write factor pairs of c = -108. They are: (-1, 108),(-2, 54),(-3, 36)...This sum is -3 + 36 = 33 = -b. The 2 real roots are -3 and 36. There is no needs for factoring.2. Tips for solving 2 special cases of quadratic equations.a. When a + b + c = 0, one real root is (1) and the other is (c/a).Example: the equation 5x^2 - 7x + 2 = 0 has 2 real roots: 1 and 2/5b. When a - b + c = 0, one real roots is (-1) and the other is (-c/a)Example: the equation 6x^2 - 3x - 9 = 0 has 2 real roots: (-1) and (9/6).3. Quadratic equations that can be factored.The standard form of a quadratic equation is ax^2 + bx + c = 0. When the Discriminant D = b^2 - 4ac is a perfect square, this equation can be factored into 2 binomials in x: (mx + n)(px + q)= 0. Solving the quadratic equation results in solving these 2 binomials for x. Students should master how to use this factoring method instead of boringly using the quadratic formula.When a given quadratic equation can be factored, there are 2 best solving methods to choose:a. The "factoring ac method" (You Tube) that determines the values of the constants m, n, p, and q of the 2 above mentioned binomials in x.b. The Diagonal Sum Method (Amazon ebook 2010) that directly obtains the 2 real roots without factoring. It is also considered as "The c/a method", or the shortcut of the factoring method. See the article titled" Solving quadratic equations by the Diagonal Sum Method" on this website.4. Quadratic equations that have 2 roots in the form of 2 complex numbers.When the Discriminant D = b^2 - 4ac < 0, there are 2 roots in the form of 2 complex numbers.5. Some special forms of quadratic equations:- quadratic equations with parameters: x^2 + mx - 7 + 0 (m is a parameter)- bi-quadratic equations: x^4 - 5x^2 + 4 = 0- equations with rational expression: (ax + b)/(cx + d) = (ex + f)- equations with radical expressions.
What are Quadratics?
Equations with an order of 2 (contains a value to the power of 2, i.e. x2). An example of a quadratic equation is: x2 + 10x + 7
What is an inequality containing the word or?
It could be the solution to some quadratic inequalities: for example x2 + 2x - 3 > 0 whose solution is x < -3 or x > 1.
What type of system equation produces the solution set infinite solution?
If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 3x + 2y = 8 6x + 4y = 16
Can Quadratic equations that can be solved using the quadratic formula also be solved by factoring?
Yes, however not all quadratic equations can easily be solved by factoring, sometimes you can factor and sometimes it is easier to use the quadratic formula. Example: x2 + 4x + 4 This can be easily factored to (x + 2)(x +2) Therefore the answer is -2 by setting x +2 = 0 and solving for x This can be done using the quadratic equation and you would get the same results, however, it was much faster to factor instead.
What is a great website to use for quadratic equations?
Wolfram Alpha can solve not just quadratic equations, but all sorts of equations. Note that in this particular website, you can see the solution for free, but you need a paid subscription to show the steps. I am sure there are other websites that can help you as well; you may want to try a Web search for "quadratic equation", for example. On the other hand, you should definitely learn to solve quadratic equations on your own.
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.
What is the reason for quadratic equations?
Many situation can be described by quadratic equations. For example, the height of an object when dropped or shot up in the air.
What does creating quadratic equations have to do with Astronomy?
Quadratic equations appear in many situations in science; one example in astronomy is the force of gravitation, which is inversely proportional to the square of the distance.
What does an overview of a math module contain?
A quick outline of the module. Topics to by taught/ but no explainations, examples,etc. Example... It may state that students will be learning how to solve quadatic equations by graphing, factoring, completing the square, and using the quadratic formula.
Are there equations that are neither linear nor quadratic?
There are many equations that are neither linear nor quadratic. A simple example is a cubic equation, such as y = x3, or a logarithmic equation, such as y = ln(x).
Do all quadratic equations have two solutions?
I may only be in 8th grade but I am absolutely positive that all quadratic equations have 2 solutions. No - They may have 0,1, or 2 answers For example, the problem x^2 + 8x +16 = 0 has only one solution -4. This is because the radical evaluates to 0 rendering the +/- sign irrelevant.
Example of quadratic function with solution?
y = ax2 + bx + c
Is it possible for a quadratic equation to have no real solution give examle ansd explain?
Is it possible for a quadratic equation to have no real solution? please give an example and explain. Thank you
What is the special cases of quadratic equation?
The standard form of a quadratic equation is: ax^2 + bx + c = 0. Depending on the values of the constants (a, b, and c), a quadratic equation may have 2 real roots, one double roots, or no real roots.There are many "special cases" of quadratic equations.1. When a = 1, the equation is in the form: x^2 + bx + c = 0. Solving it becomes solving a popular puzzle: find 2 numbers knowing their sum (-b) and their product (c). If you use the new Diagonal Sum Method (Amazon e-book 2010), solving is fast and simple.Example: Solve x^2 + 33x - 108 = 0.Solution. Roots have opposite signs. Write factor pairs of c = -108. They are: (-1, 108),(-2, 54),(-3, 36)...This sum is -3 + 36 = 33 = -b. The 2 real roots are -3 and 36. There is no needs for factoring.2. Tips for solving 2 special cases of quadratic equations.a. When a + b + c = 0, one real root is (1) and the other is (c/a).Example: the equation 5x^2 - 7x + 2 = 0 has 2 real roots: 1 and 2/5b. When a - b + c = 0, one real roots is (-1) and the other is (-c/a)Example: the equation 6x^2 - 3x - 9 = 0 has 2 real roots: (-1) and (9/6).3. Quadratic equations that can be factored.The standard form of a quadratic equation is ax^2 + bx + c = 0. When the Discriminant D = b^2 - 4ac is a perfect square, this equation can be factored into 2 binomials in x: (mx + n)(px + q)= 0. Solving the quadratic equation results in solving these 2 binomials for x. Students should master how to use this factoring method instead of boringly using the quadratic formula.When a given quadratic equation can be factored, there are 2 best solving methods to choose:a. The "factoring ac method" (You Tube) that determines the values of the constants m, n, p, and q of the 2 above mentioned binomials in x.b. The Diagonal Sum Method (Amazon ebook 2010) that directly obtains the 2 real roots without factoring. It is also considered as "The c/a method", or the shortcut of the factoring method. See the article titled" Solving quadratic equations by the Diagonal Sum Method" on this website.4. Quadratic equations that have 2 roots in the form of 2 complex numbers.When the Discriminant D = b^2 - 4ac < 0, there are 2 roots in the form of 2 complex numbers.5. Some special forms of quadratic equations:- quadratic equations with parameters: x^2 + mx - 7 + 0 (m is a parameter)- bi-quadratic equations: x^4 - 5x^2 + 4 = 0- equations with rational expression: (ax + b)/(cx + d) = (ex + f)- equations with radical expressions.
Can you give me an example of a real life situation involving quadratic functions?
Quadratic functions will be used in chemistry in real life. Quadratic equations are used to solve equilibrium problems and determine the amount of reactants in a mixture that will react and the concentrations of products that will be form.
