Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 2

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IMPORTANT

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If $p$ and $q$ are non-zero constants, the equation $x^{2} + p x + q = 0$ has roots $α$ and $β$ , then the equation $q x^{2} + p x + 1 = 0$ has roots

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Important Questions on Quadratic Equations and Inequalities

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 3

If one root is

n

times the other root of quadratic equation

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

, then

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 4

The value of

k

for which one of the roots of

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

is double of one of the roots of

x^{2} - x + k = 0

is

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 5

If the roots of

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

are in the ratio

m : n

, 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 6

If

2^{2 x} - 2^{x - 1} = 14

, then

x^{x}

is equal to

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 7

If

α

and

β

are the roots of the equation

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

, then the equation whose roots are

\frac{1}{α + β}, \frac{1}{α} + \frac{1}{β}

is equal to

EASY

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IMPORTANT

Pathfinder NDA / NA National Defence Academy and Naval Academy Entrance Examination Mathematics>Chapter 9 - Quadratic Equations and Inequalities>PRACTICE EXERCISE>Q 8

If the roots of the equation

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

are of the form

\frac{k + 1}{k}

and

\frac{k + 2}{k + 1}

, then

(a + b + c)^{2}

is equal to

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 9

If the roots of the equation,

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

are real and distinct and they differ by at most

2 m

, then

b

lies in the interval

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 10

If

a, b

and

c \in R

and

a + b + c = 0

, then the quadratic equation

4 a x^{2} + 3 b x + 2 c = 0

has