1
If x = 2 + 2 ^ (1/3) + 2 ^ (2/3), then the value of (x^3 - 6x^2 + 6x) ...
Number System Inequalities and Theory of Equations
2
The least value of the expression (x^2 + 4y^2 + 3z^2 - 2x - 12y - 6z + ...
Number System Inequalities and Theory of Equations
3
Number of positive integers (n) for which (n^2 + 96) is a perfect squa ...
Number System Inequalities and Theory of Equations
4
If x, y ∈ R satisfy the equation x² + y²-4x-2y+5=0, then the value of ...
Number System Inequalities and Theory of Equations
5
The number of real roots of the equation (x^2 - 3|x| + 2 = 0) is: ...
Number System Inequalities and Theory of Equations
6
If (x = 1 + i) is a root of the equation (x^3 -ix+1-1= 0), then the ot ...
Number System Inequalities and Theory of Equations
7
The number of roots of the equation ( x - 2)^.5(x^2 - 4x + 3) = 0 ) is ...
Number System Inequalities and Theory of Equations
8
If the expression (x^2 + 2(a + b + c)x + 3(bc + ca + ab)) is a perfect ...
Number System Inequalities and Theory of Equations
9
Let ( p ) and ( q ) be roots of the equation ( x^2 - 2x + A = 0 ) and ...
Number System Inequalities and Theory of Equations
10
The number of irrational roots of the equation {4x}/{x^2+x+3} + {5x}/{ ...
Number System Inequalities and Theory of Equations
11
Let a, b, and c be real numbers such that 4a + 2b + c = 0 and ab > 0. ...
Number System Inequalities and Theory of Equations
12
If ( a, b ) are the roots of the equation ( x^2 - 2x + 3 = 0 ), then t ...
Number System Inequalities and Theory of Equations
13
If ( alpha, beta ) are the roots of the equation ( 2x^2 - 35x + 2 = 0 ...
Number System Inequalities and Theory of Equations
14
If a, b, c are three distinct positive real numbers, then the number o ...
Number System Inequalities and Theory of Equations
15
If ( p(q-r)x^2 + q(r-p)x + r(p-q) = 0 ) has equal roots, then ( {2}/{q ...
Number System Inequalities and Theory of Equations
16
Let ( a notequal 0 ) and ( p(x) ) be a polynomial of degree greater th ...
Number System Inequalities and Theory of Equations
17
The quadratic ( x^2 + ax + b + 1 = 0 ) has roots which are positive in ...
Number System Inequalities and Theory of Equations
18
The sum of values of ( x ) satisfying the equation ( 31+8(15)^.5) ^(x^ ...
Number System Inequalities and Theory of Equations
19
If ( alpha, beta ) be the roots of the equation ( ax^2 + bx + c = 0 ), ...
Number System Inequalities and Theory of Equations
20
If ( a, b, c, d in ε{R} ), then the equation ( (x^2 + ax -3b)(x^2 - cx ...
Number System Inequalities and Theory of Equations
21
If ( alpha ) and( beta ) are the roots of the equation ( x^2 + px + q ...
Number System Inequalities and Theory of Equations
22
If ( alpha ) and ( beta ) are the roots of the equation ( x^2 + px + q ...
Number System Inequalities and Theory of Equations
23
If the roots of the equation ( (a-1)(x^2 + x + 1)^2 = (a + 1)(x^4 + x^ ...
Number System Inequalities and Theory of Equations
24
If ( b1.b2 = 2(c1 + c2) ), then at least one of the equations ( x^2 + ...
Number System Inequalities and Theory of Equations
25
The integral values of ( m ) for which the roots of the equation ( mx^ ...
Number System Inequalities and Theory of Equations
26
Suppose ( A, B, C ) are defined as ( A = a^2b + ab^2 - a^2c - ac^2 ), ...
Number System Inequalities and Theory of Equations
27
The coefficient of ( x ) in the equation ( x^2 + px + q = 0 ) was wron ...
Number System Inequalities and Theory of Equations
28
If ( a(p+q)^2 + 2bpq + c = 0 ) and ( a(p+r)^2 + 2bpr + c = 0 ) (( a no ...
Number System Inequalities and Theory of Equations
29
If the roots of the equation ( ax^2 -bx + c = 0 ) are ( α, β ), then ...
Number System Inequalities and Theory of Equations
30
If ( α) and ( β ), ( α ) and (gamma ), ( α ) and ( delta ) are the r ...
Number System Inequalities and Theory of Equations
31
The expression ( x^2 - xy + y^2 - 4x - 4y + 16 =0 ) represents: ...
Number System Inequalities and Theory of Equations
32
If (α ) and ( β) are the non-zero roots of ( ax^2 + bx + c = 0 ) and ( ...
Number System Inequalities and Theory of Equations
33
If the roots of the equation ( ax^2 + bx + c = 0 ) are of the form ( ( ...
Number System Inequalities and Theory of Equations
34
If ( α, β ) are the roots of ( ax^2 + bx + c = 0 ) and ( α + h, β + h ...
Number System Inequalities and Theory of Equations
35
If ( α, β) are the roots of the equation ( (x-a)(x-b) + c = 0 ) (( c ...
Number System Inequalities and Theory of Equations
36
If ( α, β ) are the roots of ( ax^2 + c = bx ), then the equation ( (a ...
Number System Inequalities and Theory of Equations
37
If the roots of the equation ( x^2 + 2ax+b = 0 ) are real and distinct ...
Number System Inequalities and Theory of Equations
38
If the ratio of the roots of ( ax^2 + 2bx+c=0 ) is the same as the rat ...
Number System Inequalities and Theory of Equations
39
If one root of ( x^2 - x - k = 0 ) is the square of the other, then ( ...
Number System Inequalities and Theory of Equations
40
If (α) and (β ) are the roots of the equation ( x^2 - px - 1/{2p^2} = ...
Number System Inequalities and Theory of Equations
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