Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 34

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If $b^{2} - 4 a c \leq 0$ ( where $a \neq 0$ and $a, b, c, x, y \in R$ ) satisfies the system $a x^{2} + x (b - 3) + c + y = 0$ and $a y^{2} + y (b - 1) + c + 3 x = 0$ , then value of $(\frac{y}{x})$ is

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Important Questions on Theory of Equations

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 35

If

(a^{2} + 14 a + 13) x^{2} + (a + 2) x - 2 = 0

does not have two distinct real roots, then the maximum value of

a^{2} - 15 a

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 36

Let

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

be a quadratic equation

(p, q, r \in R)

such that its roots are

α

and

β

. If

p + q + r < 0

,

p - q + r < 0

and

r > 0

, then the value of

[α] + [β]

is (where

[x]

denotes the greatest integer

x

)

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 37

Let

x^{2} + y^{2} + x y + 1 \geq a (x + y) \forall x, y \in R,

then the number of possible integer

(s)

in the range of

a

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 38

f : R \to R, f (x) = (\frac{3 x^{2} + m x + n}{x^{2} + 1})

. If the range of this function is

[- 4, 3),

then the value of

|m + n|

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 39

If

a, b, c

are non-zero real numbers, then the minimum value of the expression

(\frac{(a^{4} + 3 a^{2} + 1) (b^{4} + 5 b^{2} + 1) (c^{4} + 7 c^{2} + 1)}{a^{2} b^{2} c^{2}})

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 40

If

a, b \in R

such that

a + b = 1

and

(1 - 2 a b) (a^{3} + b^{3}) = 12 .

The value of

(a^{2} + b^{2})

is equal to

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 41

If the cubic equation

2 x^{3} - 9 x^{2} + 12 x + k = 0

has two equal roots then maximum value of

|k|

is

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Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 2 - Theory of Equations>Exercises>Q 42

Let

a, b

and

c

be distinct non-zero real numbers such that

\frac{1 - a^{3}}{a} = \frac{1 - b^{3}}{b} = \frac{1 - c^{3}}{c} .

The value of

(a^{3} + b^{3} + c^{3})

is