You are searching about How To Solve An Equation Using The Quadratic Formula, today we will share with you article about How To Solve An Equation Using The Quadratic Formula was compiled and edited by our team from many sources on the internet. Hope this article on the topic How To Solve An Equation Using The Quadratic Formula is useful to you.

The Theory of Quadratic Equations

A quadratic equation is a second-order polynomial equation. A quadratic equation has two roots. The roots can also be equal and equal. 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 generalized quadratic equation as X*X + B/A * X + C/A = 0.

The factored equation can be rewritten as X * X -X (R1 + R2) + R1R2 = 0.

Combining like terms we can see that -(R1 + R2) = B/A

R1R2 = C/A

(R1 + R2) = -B/A

Let’s examine 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)

DISCRIMINANT = 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 complete frame of A(R1-R2). So if the discriminant becomes negative it means that the quadratic equation does not have real roots because 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 we subtract A(R1-R2) from -B ie 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 + squareoot(differential)) / 2A and R2 is (-B – squareoot(differential) / 2A

Let’s take a look at some common factoring problems you may encounter

say x * x + 5 * x + 6 = 0.

The first step is to evaluate the discriminant equal to SQUAREROOT(25 – 24) = 1, which means there are real roots.

The roots of the equation are (-5 + 1)/2 equal to -2 and (-5 -1)/2 is equal to -3.

The equation can be calculated as (X+2)(X+3) = 0.

Let’s take another example

3 * x * x + 9 * x + 6 = 0, rewrites this as x * x + 3 * x + 2 = 0.

discriminant = sqrt(9-8) = 1

R1 = -1 and R2 is -2. So the factored form of the same equation is

(x + 1) (x + 2) = 0.

A quadratic equation can also be graphed. When plotted it will give the equation of the parabola.

Video about How To Solve An Equation Using The Quadratic Formula

You can see more content about How To Solve An Equation Using The Quadratic Formula on our youtube channel: Click Here

Question about How To Solve An Equation Using The Quadratic Formula

If you have any questions about How To Solve An Equation Using The Quadratic Formula, please let us know, all your questions or suggestions will help us improve in the following articles!

The article How To Solve An Equation Using The Quadratic Formula was compiled by me and my team from many sources. If you find the article How To Solve An Equation Using The Quadratic Formula helpful to you, please support the team Like or Share!

Rate Articles How To Solve An Equation Using The Quadratic Formula

Rate: 4-5 stars
Ratings: 2209
Views: 24673619

Search keywords How To Solve An Equation Using The Quadratic Formula

How To Solve An Equation Using The Quadratic Formula
way How To Solve An Equation Using The Quadratic Formula
tutorial How To Solve An Equation Using The Quadratic Formula
How To Solve An Equation Using The Quadratic Formula free
#Theory #Quadratic #Equations

Source: https://ezinearticles.com/?The-Theory-of-Quadratic-Equations&id=7557712

Có thể bạn quan tâm: