Formula To Solve Quadratic Equation Problems

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 = [(-b ± √(b2-4ac))/2a]

quadratic equations formulas

Formulas of Quadratic Equations & Method to Solve 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 (b/2)²

For example – x²+ 6x +7

Here x² =1, b= 4
(b/2)² = (4/2)² = 4
x²+4x+4 = -1+4
(x+2)² = 3
Take the square of both side
x+2 = ±√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 -b/a, and the product of the roots will be 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.

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