Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 6

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If both roots of the equation $x^{2} - 2 a x + a^{2} - 1 = 0$ lies strictly between $- 3$ and $4,$ then $[a]$ can be, where $[.]$ represents the greatest integer function

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Important Questions on Quadratic Equations

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 7

Let

α, β

be the roots of

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

and

γ, δ

be the roots of

x^{2} - 36 x + B = 0 .

If

α, β, γ, δ

forms an increasing

G . P .

Then

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 8

For the equation

x^{\frac{3}{4} {(\log_{2} x)}^{2} + \log_{2} x - \frac{5}{4}} = \sqrt{2},

which one of the following is true?

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 9

If

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

where

a c \neq 0

then

f (x) \cdot g (x) = 0

has

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 10

The value of a for which the equation

x^{2} + a x + a^{2} + 6 a < 0

is satisfied for all

x \in (1, 2)

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 11

If the roots of the equation

\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}

are equal in magnitude but opposite in sign and its product is

α

.

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 12

The integral values of a for which the equation

(a + 2) x^{2} + 2 (a + 1) x + a = 0

will have both roots integers

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 13

If

(x - 1)^{2}

is a factor of

a x^{3} + b x^{2} + c,

then roots of the equation

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

may be

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Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 14

If

b^{2} \geq 4 a c

for the equation

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

, then all roots of the equation will be real if