Mathematics · JEE

Relations between roots and coefficients, nature of roots Concepts for JEE

12+ syllabus-aligned questions available

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Master Relations between roots and coefficients, nature of roots by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

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Concept explainer

Relations between roots and coefficients, nature of roots is a core JEE Main Mathematics subtopic under Complex Numbers and Quadratic Equations. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of Relations between roots and coefficients, nature of roots in the JEE syllabus
Memorise key formulas and standard results linked to Relations between roots and coefficients, nature of roots
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise Relations between roots and coefficients, nature of roots with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to Relations between roots and coefficients, nature of roots and reattempt after 48 hours

Common trap

Students often rush Relations between roots and coefficients, nature of roots questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Complex Numbers and Quadratic Equations in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 2: Complex Numbers and Quadratic Equations

x+\frac{1}{x}=4,

then

x^{4}+\frac{1}{x^{4}}

is equal to

Q2MathsUnit 2: Complex Numbers and Quadratic Equations

If the product of two numbers is 10 and their sum is

7,

which is the greatest of the two numbers?

Q3MathsUnit 2: Complex Numbers and Quadratic Equations

The zeros of the polynomial

n^{3}+9 n^{2}+

23 n+15

are

a-d, a

and

a+d .

What is the value of 'a'?

Q4MathsUnit 2: Complex Numbers and Quadratic Equations

Discriminant of the equation

-3 x^{2}+

2 x-8=0

Q5MathsUnit 2: Complex Numbers and Quadratic Equations

If the sum of the roots of the equation

a x^{2}+b x+c=0

is equal to sum of the squares of their reciprocals, then

b c^{2}, c a^{2}, a b^{2}

are in

Q6MathsUnit 2: Complex Numbers and Quadratic Equations

x-y=7

and

x^{3}-y^{3}=133 ;

find: the value of

x y

Q7MathsUnit 2: Complex Numbers and Quadratic Equations

Find

p \in R

for

x^{2}-p x+p+3=0

has

Q8MathsUnit 2: Complex Numbers and Quadratic Equations

Assertion Let equations

a x^{2}+b x+c=

\mathbf{0}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \in \boldsymbol{R}) \& \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0}

have common root, then

\frac{\boldsymbol{a}+\boldsymbol{c}}{\boldsymbol{b}}=\frac{\mathbf{1}}{\mathbf{3}}

Reason If both roots of

A x^{2}+B x+K_{1}=0 \&

\boldsymbol{A}^{\prime} \boldsymbol{x}^{2}+\boldsymbol{B}^{\prime} \boldsymbol{x}+\boldsymbol{K}_{2}=\mathbf{0}

are identical

\operatorname{then} \frac{\boldsymbol{A}}{\boldsymbol{A}_{1}}=\frac{\boldsymbol{B}}{\boldsymbol{B}_{1}}=\frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}}\left(\text { where } \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{K}_{1}\right.

and

\left.A^{\prime}, B,^{\prime} K_{2} \in R\right)

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