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Equation:

An equation is a mathematical sentence that uses the equal sign (=) to show that two expressions are equal.

Example 1:  3+4=7 ;  Example 2: 3a+4b=1

 

Linear Equation:

An equation is said to be linear, in which the highest power of each variable is one and there is no term involving the product of the variables.

Example ax+by+c = 0; where a,b ≠ 0

 

Quadratic Equation:

An equation is said to be quadratic, in which the highest power of the variable is two.

Example ax²+bx+c = 0; where a,b,c are numbers and a ≠ 0

 

Take Away:

1. Every Quadratic equation gives two values of the unknown variable and these values are called roots of the equation.
2. If α and β satisfies the quadratic equation ax²+bx+c = 0, then α and β are the roots of this equation.                                                     Sum of roots α+β = -b/a = – (coefficient of x) / (coefficient of x²) Product of roots αβ = c/a = (constant term) / (coefficient of x²)
3. If roots are α and β then quadratic equation will be x²-(α+β)x+αβ=0
4. If general quadratic equation is given by ax²+bx+c = 0, then solution of this equation can be find by using quadratic formula.                                                                                                                                                                                        x= [-b ± √(b²-4ac)] / 2a  where, b²-4ac is called discriminant ‘D’

 

Nature of Roots:

As Discriminant ‘D’ = b²-4ac; here a, b, c are real numbers, a≠0:

1. If D = b² -4ac = 0, then roots are real and equal.
2. If D = b² -4ac > 0, then roots are real and unequal.
3. If D = b² -4ac < 0, then roots are Imaginary.

Find More Examples on Nature of Roots ClickHere

Lets attempt one quiz on Quadratic Equations BasicLevel