A quadratic equation is a polynomial equation which includes a variable with a high degree. In algebra, the equation includes some numbers and a variable. The value of a variable is lies between the quadrates. The number of values of the variable is completely dependent on the degree of it. If the equation includes a higher degree of two than there are 2 values are available of unknowns. To solve quadratic equations, you need to follow some rules, but it usually takes more time. In competitive exams, the time plays an important role to qualify it. We cannot spend a lot of time on single questions. That is why it is best to know the tricks to solve quadratic equations.
Before going to solve any example, first, understand the basics of it,
Consider some example like
In the first equation, the higher degree of a variable is 2, and in the second one, the higher degree is 3. So we may get the value of x 2 and 3 respectively.
The standard form of quadratic equation is ax²+bx+c=0
So, we can find out the value of x by the formula as, X =
If we consider the second 2x³
+12x +8=0 then it can be solved by above
The values a, b and c According to the standard form of a quadratic equation, the value is found as compare both standard and question questions.
After comparing the equation we have a = 2, b = 12 and c = 8
Put the values of a, b, and c. You will get the value of x. The positive and negative sign shows two values of the single variables.
Now you have two values of x that is positive (-3+√80) and (-3-√80)
But it is the complex method to solve the equation and takes a lot of time to solve quadratic equations. If you need to solve these equations in the least time duration or within a minute, then use some tricks. The trick can help you to solve it in the least time.
First consider there some sign to get their answers.
If you have equation like
+ bx + c= 0
ax²+ bx -c= 0
ax²- bx + c= 0
ax²- bx –c =0
Consider these signs to know their value signs.
First equation variable values include (-, -)
2nd includes (- , +)
3rd includes (+, +)
4th includes (+,-)
Consider an example to understand this trick to solve quadratic equations.
Now find the coefficient by multiplying x²and 3 coefficients. 2x3 may write as 6x1, and the result will be achieved by 6 and -1
The final root may divide by the 2 which is the x²
Now you have 6/2 and -1/2
You have roots (3, 0.5)
But the sign shows (-, +) and according to the trick you must have root (-3, 0.5)
This is a very short trick to get the root of unknown variables. The trick needs to only 30 to 60 seconds to solve quadratic equations. If you are looking the best method to solve quadratic problems in less than a minute then must apply this trick which requires least time.