EASY

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IMPORTANT

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If one root of the equation $a x^{2} + b x + c = 0, a \neq 0$ is reciprocal of the other root, then which one of the following is correct?

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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 16

p, q, r

are rational numbers, then the roots of the equation

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

are

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 17

If the roots of the equation

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

are equal, then which one of the following is 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 18

Consider the equation

(x - p) (x - 6) + 1 = 0

having integral coefficients. If the equation has integral roots, then what values can

p

have?

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 19

α

and

β

be the roots of the equation

x^{2} + x + 1 = 0

. Then, the equation whose roots are

α^{19}

and

β^{7}

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 21

α, β

are the roots of the quadratic equation

x^{2} - x + 1 = 0

, then which one of the following is 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 22

If the roots of

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

are

\sin α

and

\cos α

for some

α

, then which one of the following is 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 23

(x + a)

is a factor of both the quadratic polynomials

x^{2} + p x + q

and

x^{2} + l x + m

, where

p, q, l

and

m

are constants, then which one of the following is correct?

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 24

Let

α

and

γ

be the roots of

A x^{2} - 4 x + 1 = 0

and

β

and

δ

be the roots of

B x^{2} - 6 x + 1 = 0

. If

α, β, γ

and

δ

are in

HP

, then what are the values of

A

and

B

respectively?

If one root of the equation ax2+bx+c=0, a≠0 is reciprocal of the other root, then which one of the following is correct?

Important Questions on Quadratic Equations and Inequalities

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If one root of the equation $a x^{2} + b x + c = 0, a \neq 0$ is reciprocal of the other root, then which one of the following is correct?