Quadratic Equations

Quadratic Equations

Solving quadratic equations is the most fundamental concept of mathematics. Using quadratic formula may be very useful and efficient to crack questions containing big dirty equations and have them solved in minutes.

Importance

Observing a general trend in every competetive exam, there is atleast a sure shot question from this topic every year. Secondly, ther are high chances that solving simple equations can be a part of a question based on any other topic so it is compulsory to have its knowledge.

Quadratic Formula:

A standard quadratic equation is of the form !!ax^2+bx+c=0!! and its roots are given by:

!!x=(-b+-sqrt(b^2-4ac))/(2a)!!

This is the key formula of this topic and all probable questions can be solved using this. Some more concepts mentioned below should be kept in mind since these types questions occur frequently.

Nature of roots:

For the standard equation !!ax^2+bx+c=0!!
Discriminant !!(D)=!!!!b^2-4ac!!
(i) For real and distinct roots, !!D>0 !!
(ii) For imaginary roots, !!D<0!!
(iii) For real and equal roots, !!D=0!!

Relation between coefficients and roots:

For the standard equation !!ax^2+bx+c=0!!, let !!p and q!! be the roots of the equation:

Sum of roots: !!p+q=-b/a!!
Product of roots : !!pq=c/a!!

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