Mathematics · JEE

Important Questions: Relations between roots and coefficients, nature of roots for JEE

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Syllabus context

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

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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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Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

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Key areas include Relations between roots and coefficients, nature of roots. Prioritise these before moving to edge cases.

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Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

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