Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 29

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

If the sum of the roots of the quadratic equation $a x^{2} + b x + c = 0$ is equal to the sum of the squares of their reciprocals, then $\frac{a}{c}, \frac{b}{a}$ and $\frac{c}{b}$ are in

50% studentsanswered this correctly

Important Questions on Quadratic Equations

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 30

If

a, b

are real and unequal, then the roots of the quadratic equation

(a - b) x^{2} - 5 (a + b) x - 2 (a - b) = 0

are

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 31

The roots

x_{1}

and

x_{2}

of the equation

x^{2} + p x + 12 = 0

are such that their difference is

1 .

Then the positive value of

p

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 33

Let

α

and

β

be the real roots of the equation

x^{2} - x (λ - 2) + (λ^{2} + 3 λ + 5) = 0 .

The maximum value of

α^{2} + β^{2}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 34

If

a

and

b

are the non-zero roots of equation

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

then

(a + b)

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 35

(α_{1}, α_{2}), (α_{2}, α_{3})

and

(α_{3}, α_{1})

are respectively the roots of

x^{2} - 2 a x + 2 = 0, x^{2} - 2 b x + 3 = 0

and

x^{2} - 2 c x + 6 = 0 .

If

α_{1}, α_{2}, α_{3} \in R^{+},

then the value of

a + b + c

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 36

The number of irrational roots of the equation

\frac{4 x}{x^{2} + x + 3} + \frac{5 x}{x^{2} - 5 x + 3} = - \frac{3}{2}

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 37

For all

x \in (- 2, 3)

number of solutions of the equation

{(x^{2} + x + 1)}^{2} + 1 = (x^{2} + x + 1) (x^{2} - x - 5)

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 38

The value of

m

for which one of the roots of

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

is double of one of the roots of

x^{2} - x + m = 0

is