JEE Quadratic Equations- Advanced Conceptual Understanding
This page will teach you how to master JEE Quadratic Equations up to JEE Advanced level. We highlight the main concepts, provide a list of examples with solutions, and include problems for you to try. Once you are confident, you can take the quiz to establish your mastery.
A root of the equation is a number (real or complex), say , which satisfies the equation i.e. . The roots of the quadratic equation with are given by .
JEE Conceptual Theory
To have mastery over Quadratic Equations of JEE Advanced, the main concepts you should be confident of are polynomial equations reducible to quadratic equations, algebraic interpretation of Rolle's theorem, intermediate value theorem and analysis of cubic equation with real coefficients.
Polynomial equations reducible to quadratic equations
An equation of the form
An equation of the form , where
An equation of the form
An equation of the form and : Substitute
Reciprocal equations: or
Algebraic interpretation of Rolle's theorem
Between any two roots of a polynomial equation , there always exists a roots of its derivative
Relation between roots and derivatives
Some important deductions from Rolle's theorem
Intermediate Value Theorem
If is a polynomial function such that , then takes every value between and
If and are of opposite signs, then one root of the equation must lie between and
Analysis of cubic equation with real coefficients
Condition for all three real roots of a cubic equation
Condition for two real roots and one complex root
Trigonometrical method of solving cubic equation
JEE Mains Problems
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JEE Advanced Problems
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Once you are confident of Quadratic Equations, move on to JEE Complex Numbers.