You are searching about How To Solve A Quadratic Equation By Quadratic Formula, today we will share with you article about How To Solve A Quadratic Equation By Quadratic Formula was compiled and edited by our team from many sources on the internet. Hope this article on the topic How To Solve A Quadratic Equation By Quadratic Formula is useful to you.
Muc lục nội dung
The Theory of Quadratic Equations
A quadratic equation is a polynomial equation of the second order. A quadratic equation has two roots. Roots can also be equal and even. Let’s write the quadratic equation in two ways
AX * X + BX + C = 0 an example of a quadratic equation would be 5X*X + 3 *X + 2 = 0
Let’s rewrite the quadratic equation as (X-R1) * (X-R2) = 0. The above step is called factoring.
Let’s rewrite the original quadratic equation as X*X + B/A * X + C/A = 0
The equation can be rewritten as X * X – X( R1 + R2) + R1R2 = 0.
Comparing like terms we can see that -(R1 + R2) = B/A
R1R2 = C/A
(R1 + R2) = -B/A
Let’s investigate B* B – 4 * A * C
B = -A (r1 + r2)
C = AR1R2; 4*A*C = 4*A*A*R1*R2
B*B = A*A(R1 + R2) * (R1 + R2)
DIVISION = A*A(R1 + R2) * (R1 + R2) – 4*A*A*R1*R2
= A*A ( (R1+R2)((R1+R2) – 4R1R2)
= A*A (R1 – R2) * (R1 – R2).
Note that this is a perfect square of A(R1-R2). So if the discalment is negative it means that the quadratic equation has no real roots as the squares of real numbers are also perfect squares.
Let’s add A(R1-R2) to B which is A(R1 + R2), and the sum is 2AR1. Dividing this by 2A will yield R1.
Similarly let’s take A(R1-R2) from B i.e., A(R1 + R2) – A (R1-R2)
which is equal to A(2R2) or 2AR2. Dividing this by 2A will yield R2.
So R1 is (-B + squareroot( calucal) / 2A and R2 is (-B – squareroot( calulo) / 2A
Let’s take a look at some common problems you may encounter
say x * x + 5*x + 6 = 0.
The first step tested the discriminant equal to SQUAREROOT(25 – 24) = 1, which means there are true roots.
The roots of the equation are (- 5 + 1)/ 2 equals -2 and (-5 -1)/2 equals -3.
The equation can be expressed as (X+2)(X+3) = 0.
Let’s take another example
3 * x * x + 9 * x + 6 = 0, rewriting this as x * x + 3*x + 2 = 0.
quotient = sqrt(9-8) = 1
R1 = -1 and R2 is 2. So the integrated form of the same equation
(x + 1)(x+ 2) = 0.
A quadratic equation can also be plotted on a graph. When plotted it will produce the equation of a parabola.
Video about How To Solve A Quadratic Equation By Quadratic Formula
You can see more content about How To Solve A Quadratic Equation By Quadratic Formula on our youtube channel: Click Here
Question about How To Solve A Quadratic Equation By Quadratic Formula
If you have any questions about How To Solve A Quadratic Equation By Quadratic Formula, please let us know, all your questions or suggestions will help us improve in the following articles!
The article How To Solve A Quadratic Equation By Quadratic Formula was compiled by me and my team from many sources. If you find the article How To Solve A Quadratic Equation By Quadratic Formula helpful to you, please support the team Like or Share!
Rate Articles How To Solve A Quadratic Equation By Quadratic Formula
Rate: 4-5 stars
Ratings: 4138
Views: 42377889
Search keywords How To Solve A Quadratic Equation By Quadratic Formula
How To Solve A Quadratic Equation By Quadratic Formula
way How To Solve A Quadratic Equation By Quadratic Formula
tutorial How To Solve A Quadratic Equation By Quadratic Formula
How To Solve A Quadratic Equation By Quadratic Formula free
#Theory #Quadratic #Equations
Source: https://ezinearticles.com/?The-Theory-of-Quadratic-Equations&id=7557712