Mathematics · JEE

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

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Master Relations between roots and coefficients, nature of roots through exam-style multiple-choice questions. This page features 12+ JEE MCQs covering Relations between roots and coefficients, nature of roots, each with verified answers and clear explanations.

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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