Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 74

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If $a_{1}, a_{2}, a_{3} \dots a_{n}, A_{1}, A_{2}, A_{3}, \dots, A_{n}, k$ are all real numbers $(k \neq 0)$ and number of imaginary roots of the equation $\frac{A_{1}^{2}}{x - a_{1}} + \frac{A_{2}^{2}}{x - a_{2}} + \dots . . . . . . + \frac{A_{n}^{2}}{x - a_{n}} = k$ is $α$ . Then find the value of $α + 15$

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Important Questions on Quadratic Equations

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 1

The set of all real numbers

x

for which

x^{2} - |x + 2| + x > 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 2

Find the range of values of

' t'

for which

2 \sin t = \frac{1 - 2 x + 5 x^{2}}{3 x^{2} - 2 x - 1}, t \in [- \frac{π}{2}, \frac{π}{2}] .

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 3

In a triangle

P Q R, ∠ R = \frac{π}{2}

. If

\tan (\frac{P}{2})

and

\tan (\frac{Q}{2})

are the roots of

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

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 5

Let

p

and

q

be real numbers such that

p \neq 0, p^{3} \neq q

and

p^{3} \neq - q

. If

α

and

β

are non zero complex numbers satisfying

α + β = - p

and

α^{3} + β^{3} = q

, then a quadratic equation having

\frac{α}{β}

and

\frac{β}{α}

as its roots is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 6

Let

α

and

β

be the roots of

x^{2} - 6 x - 2 = 0

, with

α > β

. If

a_{n} = α^{n} - β^{n}

for

n \geq 1

, then the value of

\frac{a_{10} - 2 a_{8}}{2 a_{9}}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 7

The quadratic equation

p (x) = 0

with real coefficients has purely imaginary roots. Then the equation

p (p (x)) = 0

has?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 8

Let

S

be the set of all non-zero real numbers

α

such that the quadratic equation

α x^{2} - x + α = 0

has two distinct real roots

x_{1}

and

x_{2}

satisfying the inequality

|x_{1} - x_{2}| < 1

. Which of the following intervals is (are) a subset(s) of

S

?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 9

Let

- \frac{π}{6} < θ < - \frac{π}{12} .

Suppose

α_{1}

and

β_{1}

are the roots of the equation

x^{2} - 2 x \sec θ + 1 = 0

and

α_{2}

and

β_{2}

are the roots of the equation

x^{2} + 2 x \tan θ - 1 = 0 .

If

α_{1} > β_{1}

and

α_{2} > β_{2},

then

α_{1} + β_{2}

equals?