Gamma Question Bank for Engineering Mathematics>Chapter 3 - Quadratic Equations>Assignment>Q 4

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If the quadratic equations $x^{2} + p q x + r = 0$ and $x^{2} + p r x + q = 0$ have a common root then the equation containing their other roots is/are

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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 5

The quadratic equation $x^{2}-(m-3) x+m=0$ has

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

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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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