We all have used the quadratic equation Derivation in solving the quadratic equation but only a few of us might have wondered about quadratic equation derivation. If you are wondering about the same then we are going to break it down the quadratic equation formula mystery for you.
Quadratic Equation is basically an equation that has the typical form as ax^2+bx+c= 0. Here we basically have the x as the unknown and a,b,c as the known values. So we basically have to find out the value of x in our whole quadratic equation. We use the quadratic equation formula to find the solution of the equation and subsequently the value of x.
Quadratic Equation Derivation for Formula
Well, we know that the quadratic equation formula works just like magic to find the solution to any standard quadratic equation. The formula has been developed by the mathematician Shridharacharya and is written as x = [-b ± √(b² – 4ac)]/2a, With this formula, you can find the solution of any standard simple quadratic equation just by placing the values.
We are here going to derive the quadratic equation formula for all our scholar readers. Most of them wonder as to how this formula is derived so they can a look at the same below.
- First of all, we basically need to complete the square in the quadratic equation ax^2+bx+c
- You can use the completing the square technique here and subsequently you will get the single “x” in the equation.
- Divide the whole equation by a and then put the c/a to the other equivalent side of the equation.
- Next just simply add (b/2a)2 to both sides of the equation.
- Now the left side will become something like x2 + 2dx + d2 and the right side will be -c/a+(b/2a)^2 .
- At last, you just need to find the value of single x here by completing the square.
- When you ultimately solve the whole equation to find the value of x then it will ultimately break out as the formula of a quadratic equation.
So, ultimately we will prove that when you solve the quadratic equation then it will turn into the quadratic equation formula. We know that both the quadratic equation formula and the equation interrelate to each other. That will work as the answer to the demand of the question. Kindly share the article with other scholars as well who want to learn to derive the quadratic equation formula.
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