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Q.) If the roots of the equation ( (a-1)(x^2 + x + 1)^2 = (a + 1)(x^4 + x^2 + 1) ) are real and distinct then the value of ( a ) is:
[A]
(-infty, 3]
[B]
(-infty, 2) union(2, infty)
[C]
[-2, 2]
[D]
[-3, infty)
[A] (-infty, 3]
[B] (-infty, 2) union(2, infty)
[C] [-2, 2]
[D] [-3, infty)
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Number System Inequalities and Theory of Equations 📚
1
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2
If x, y ∈ R satisfy the equation x² + y²-4x-2y+5=0, then the value of the expression [(√x− y^.5)²+4√ ...
3
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4
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5
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6
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7
Let ( p ) and ( q ) be roots of the equation ( x^2 - 2x + A = 0 ) and let ( r ) and ( s ) be the roo ...
8
The number of irrational roots of the equation {4x}/{x^2+x+3} + {5x}/{x^2-5x+3} = -{3}/{2} ) is: ...
9
Let a, b, and c be real numbers such that 4a + 2b + c = 0 and ab > 0. Then the equation ax² + bx + c ...
10
If ( a, b ) are the roots of the equation ( x^2 - 2x + 3 = 0 ), then the equation whose roots are ( ...
11
If ( alpha, beta ) are the roots of the equation ( 2x^2 - 35x + 2 = 0 ), then the value of ( (2alpha ...
12
If ( a, b, c, d in ε{R} ), then the equation ( (x^2 + ax -3b)(x^2 - cx + d)(x^2 - cx + b)(x^2 -dx +2 ...
13
If ( alpha ) and ( beta ) are the roots of the equation ( x^2 + px + q = 0 ), and ( alpha )^4 and ( ...
14
If the roots of the equation ( (a-1)(x^2 + x + 1)^2 = (a + 1)(x^4 + x^2 + 1) ) are real and distinct ...
15
The coefficient of ( x ) in the equation ( x^2 + px + q = 0 ) was wrongly written as 17 in place of ...
16
If the roots of the equation ( ax^2 -bx + c = 0 ) are ( α, β ), then the roots of the equation ( b ...
17
If one root of ( x^2 - x - k = 0 ) is the square of the other, then ( k ) equals: ...
18
Let ( a notequal 0 ) and ( p(x) ) be a polynomial of degree greater than 2. If ( p(x) ) leaves remai ...
19
The quadratic ( x^2 + ax + b + 1 = 0 ) has roots which are positive integers. Then ( a^2 + b^2 ) can ...
20
The sum of values of ( x ) satisfying the equation ( 31+8(15)^.5) ^(x^2-3) = (32+8(15)^.5 )^x^2-3is: ...
21
The expression ( x^2 - xy + y^2 - 4x - 4y + 16 =0 ) represents: ...
22
If (α ) and ( β) are the non-zero roots of ( ax^2 + bx + c = 0 ) and ( α^2), ( β^2 ) are the roots o ...
23
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24
If ( α, β ) are the roots of ( ax^2 + c = bx ), then the equation ( (a + cy)^2 = b^2 y ) in ( y ) ha ...
25
If the roots of the equation ( x^2 + 2ax+b = 0 ) are real and distinct and they differ by at most ( ...
26
The least value of the expression (x^2 + 4y^2 + 3z^2 - 2x - 12y - 6z + 14) is: ...
27
Number of positive integers (n) for which (n^2 + 96) is a perfect square is: ...
28
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29
If (x = 1 + i) is a root of the equation (x^3 -ix+1-1= 0), then the other real root is: ...
30
If the expression (x^2 + 2(a + b + c)x + 3(bc + ca + ab)) is a perfect square, then: ...
31
If a, b, c are three distinct positive real numbers, then the number of real roots of ( ax^2 + 2b|x| ...
32
If ( p(q-r)x^2 + q(r-p)x + r(p-q) = 0 ) has equal roots, then ( {2}/{q} ) equals: ...
33
If ( alpha, beta ) be the roots of the equation ( ax^2 + bx + c = 0 ), then the value of ( a alpha^2 ...
34
If ( alpha ) and( beta ) are the roots of the equation ( x^2 + px + q = 0 ), and ( alpha )^4 and (be ...
35
If ( b1.b2 = 2(c1 + c2) ), then at least one of the equations ( x^2 + b1x + c1 = 0 ) and ( x^2 + b2x ...
36
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37
If the roots of the equation ( ax^2 + bx + c = 0 ) are of the form ( (k+1)/k ) and (k+2}/k+1), then ...
38
If ( α, β) are the roots of the equation ( (x-a)(x-b) + c = 0 ) (( c notequal to 0, then the roots ...
39
If the ratio of the roots of ( ax^2 + 2bx+c=0 ) is the same as the ratio of the roots of ( px^2+2qx+ ...
40
If (α) and (β ) are the roots of the equation ( x^2 - px - 1/{2p^2} = 0 ) where ( p in belongs{R} ), ...