# Formula for Quadratic Equation

## Formula For Quadratic Equation

A Quadratic Equation is the equation that can be rearranged in standard form ax^{2} + 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
**ax**^{2}+bx+c = 0 - Where, x is the unknown variable and a, b, c are the numerical coefficients.

### Quadratic Equations Formulas

- If ax
^{2}+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: x^{2} + 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 x
^{2}– (Α + Β)x + Α*Β = 0

- 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 x

**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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