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Formula For Quadratic Equation
A Quadratic Equation is the equation that can be rearranged in standard form ax2 + bx + c = 0 as where x is a variable and a, b, and c represent constants , where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.


Formulas for Quadratic Equations & Definitions
- An equation where the highest exponent of the variable is a square. Standard form of quadratic equation is ax2+bx+c = 0
- Where, x is the unknown variable and a, b, c are the numerical coefficients.
Quadratic Equations Formulas
- If ax2+bx+c = 0 is a quadratic equation, then the value of x is given by the following formula
- x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}
Formulas of Quadratic Equations & Method of Quadratic Questions
- Factorization
It is very simple method to to solve quadratic equations. Factorization give 2 linear equations
For example: x2 + 3x – 4 = 0
Here, a = 1, b = 3 and c = -4
Now, find two numbers whose product is – 4 and sum is 3.
So, the numbers are 4 and -1.
Therefore, two factors will be 4 and -1
Completing the Square Method
- Every Quadratic question has always a square term. If we could get two square terms of quality sign we can get a linear equations. Middle term is called as ‘b’ and splited by (\frac{b}{2})^2
For example : – x²+ 6x +7
Here x² =1, b= 4
(\frac{b}{2})^2 = (\frac{4}{2})^2 = 4
x²+4x+4 = -1+4
(x+2)² = 3
Take the square of both side
x+2 = ±\sqrt{3} = ± 1.73
Therefore, x = -0.27 or -3.73
Formulas of Quadratic Equations & Key points to Remember
Other basic concepts to remember while solving quadratic equations are:
1.Nature of roots
- Nature of roots determine whether the given roots of the equation are real, imaginary, rational or irrational. The basic formula is b² – 4ac.
- This formula is also called discriminant or D. The nature of the roots depends on the value of D. Conditions to determine the nature of the roots are:
- If D < 0, than the given roots are imaginary.
- If D = 0, then roots given are real and equal.
- If D > 0, then roots are real and unequal.
- Also, in case of D > 0, if the equation is a perfect square than the given roots are rational, or else they are irrational.
2. Sum and product of the roots
- For any given equation the sum of the roots will always be – \frac{b}{a} , and the product of the roots will be – \frac{c}{a} . Thus, the standard quadratic equation can also be written as x2 – (Α + Β)x + Α*Β = 0
3. Forming a quadratic equation
- The equation can be formed when the roots of the equation are given or the product and sum of the roots are given.
Read Also – Tips & tricks to solve quadratic equation question
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