Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 12

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Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots. $(4, 3) .$ Rahul made a mistake in writing down the coefficient of $x$ to get roots $(3, 2) .$ The correct roots of the equation are?

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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 13

Let for

a \neq a_{1} \neq 0

,

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

,

g (x) = a_{1} x^{2} + b_{1} x + c_{1}

and

p (x) = f (x) - g (x) .

If

p (x) = 0

only for

x = - 1

and

p (- 2) = 2,

then the value of

p (2)

is?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 14

The equation

e^{\sin x} - e^{- \sin x} - 4 = 0

has ?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 15

If the equations

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

and

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

, have a common root, then

a : b : c

is?

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 16

If

a \in R

and the equation

- 3 {(x - [x])}^{2} + 2 (x - [x]) + a^{2} = 0

(where

[x]

denotes the greatest integer

\leq x

) has no integral solution, then all possible values of

a

lie in the interval:

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 17

Let

α

and

β

be the roots of equation

{px}^{2} + qx + r = 0, p \neq 0 .

If

p, q, r

are in

A . P .

and

\frac{1}{α} + \frac{1}{β} = 4,

then the value of

|α - β|

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 18

Let

α

and

β

be the roots of equation

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

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 equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 19

The number of all possible positive integral values of

α

for which the roots of the quadratic equation,

6 x^{2} - 11 x + α = 0

are rational numbers is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-3>Q 20

If

λ

be the ratio of the roots of the quadratic equation in

x, 3 m^{2} x^{2} + m (m - 4) x + 2 = 0,

then the least value of

m

for which

λ + \frac{1}{λ} = 1,

is