EASY

NDA & NA EE

IMPORTANT

Earn 100

What is the difference in the roots of the equation $x^{2} - 10 x + 9 = 0$ ?

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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 69

a

and

b

are rational and

b

is not perfect square, then the quadratic equation with rational coefficients whose one root is

3 a + \sqrt{b}

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 70

α

and

β

are the roots of the equation

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

then what is

\frac{α^{10} + β^{10}}{α^{- 10} + β^{- 10}}

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 71

The quadratic equation

x^{2} + b x + 4 = 0

will have real roots, if

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 72

α

and

β

are the roots of the equation

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

where

a \neq 0,

then

(a α + b) (a β + b)

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 74

Every quadratic equation

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

where

a, b, c \in R, a \neq 0

has

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 75

α, β

are the roots of

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

and

α + h, β + h

are the roots of

p x^{2} + q x + r = 0,

then what is

h

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 76

Consider the following statements in respect of the given equation ${(x^{2} + 2)}^{2} + 8 x^{2} = 6 x (x^{2} + 2)$

$I .$ All the roots of the equation are complex

$II .$ The sum of all the roots of the equation is $6$

Which of the above statement(s) is/are correct?

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 77

In solving a problem that reduces to a quadratic equation, one student makes a mistake in the constant term and obtains

8

and

2

for roots. Another student makes a mistake only in the coefficient of first degree term and finds

- 9

and

- 1

for roots. The correct equation is

What is the difference in the roots of the equation x2-10x+9=0?

Important Questions on Quadratic Equations and Inequalities

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What is the difference in the roots of the equation $x^{2} - 10 x + 9 = 0$ ?