Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 30

EASY

NDA & NA EE

IMPORTANT

Earn 100

If the equations $x^{2} + 2 x + 3 λ = 0$ and $2 x^{2} + 3 x + 5 λ = 0$ have a non-zero common root, then $λ$ is equal to

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Important Questions on Quadratic Equations and Inequalities

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 31

If the equations

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

and

x^{2} + x + 1 = 0

have a common root, then

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 32

If the quadratic equations

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

and

a x^{2} + 2 b x + c = 0 (b \neq c)

have a common root, then

a + 4 b + 4 c

is equal to

MEDIUM

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 33

The range of values of

m

for which the equation

(m - 5) x^{2} + 2 (m - 10) x + m + 10 = 0

has real roots of the same sign is given by

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 34

The set of real values of

x

satisfying the inequality

|x^{2} + x - 6| < 6

is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 35

The value of

a

for which the equation

x^{2} - 2 (a - 1) x + (2 a + 1) = 0

has both roots positive is

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 36

If the roots of the equation

x^{2} - 4 x - \log_{3} N = 0

are real, then what is the minimum value of

N

?

HARD

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 37

If

a, b

and

c

are positive and are in

AP

, the roots of the quadratic equation

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

are real for

EASY

NDA & NA EE

IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 38

If the roots of equation

x^{2} - p x + (p - 1) = 0

are

r_{1}

and

r_{2}

, then minimum value of

(r_{1}^{2} + r_{2}^{2})

will be for