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JEE Questions for Maths Equations And Inequalities Quiz 14 - MCQExams.com
JEE
Maths
Equations And Inequalities
Quiz 14
If 2a + 3b + 6c = 0 then at least one root of the equation ax
2
+ bx + c = 0 lies in the interval
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(0, 1)
0%
(1, 2)
0%
(2, 3)
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(3, 4)
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Greater than of equal to α
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Equal to α
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Greater than α
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Smaller than α
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0%
0%
2)
0%
0%
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0%
–1
0%
0
0%
abc
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a + 2b + c
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None of these
The value of b for which the equations x
2
+ bx – 1 = 0 x
2
+ x + b = 0 have one root in common is
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
3
0%
2
0%
1
0%
None of these
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0%
2)
0%
0%
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1
0%
3
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5
0%
7
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0%
2, 4, 8
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3, 6, 12
0%
None of these
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
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0%
2
0%
3
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4
0%
5
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
The sum of the fourth powers of the roots of the equation x
3
+ x + 1 = 0 is
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–2
0%
–1
0%
1
0%
2
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0%
2)
0%
0%
0%
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0%
0%
2)
0%
0%
0%
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0%
2)
0%
0%
For the equation |x|
2
+ |x| – 6 = 0, the roots are
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One and only real numbers
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Real with sum one
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Real with sum zero
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Real with product zero
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0%
0%
2)
0%
0%
None of these
If the roots of the equation bx
2
+ cx + a= 0 be imaginary, then for all real values of x, the expression 3b
2
x
2
+6bcx + 2c
2
= 0 is
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Greater than 4ab
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Less than 4ab
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Greater than –4ab
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Less than –4ab
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(4, 4)
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(–4, 4)
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(4, –4)
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(–4, 4)
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Real and imaginary
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Real and equal
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Imaginary
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None of these
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0%
2)
0%
0%
None of these
If the roots of the equation qx
2
+ px + q = 0 where p, q are real, be complex, then the roots of the equation x
2
– 4qx + p
2
= 0 are
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Real and unequal
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Real and equal
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Imaginary
0%
None of these
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0%
2)
0%
0%
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0%
0%
2)
0%
0%
The coefficient of x in the equation x
2
+ px + q = 0 was taken as17 in place of 13, its roots were round to be –2 and –15, the rots of the original equation are
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0%
3, 10
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–3, –10
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–5, –18
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None of these
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0%
0%
2)
0%
0%
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b
0%
–b
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0%
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0%
2)
0%
0%
If both the roots of the quadratic equation x
2
– 2kx + k
2
+ k – 5 = 0 are less than 5, hen k lies in the interval
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(–∞, 4)
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[4, 5]
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(5, 6]
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(6, ∞)
If the roots of the equations x
2
– bx + c = 0 and x
2
– cx + b = 0 differ by the same quantity, then b + c is equal to
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4
0%
1
0%
0
0%
–4
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0%
0%
2)
0%
0%
None of these
In a triangle ABC, the value of ∠A is given by 5 cosA + 3 = 0, then the equation whose roots are sinA and tanA will be
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
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8, –1
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–9, 2
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–8, 2
0%
9, 1
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0%
0%
2)
0%
0%
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0%
2)
0%
0%
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4
0%
0
0%
6
0%
2
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0%
1
0%
0%
The product of all real roots of the equation x
2
– |x| – 6 = 0 is
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0%
–9
0%
6
0%
9
0%
36
For the equation 3x
2
+ px + 3 = 0, p > 0 if one of the root is square of the other, then p is equal to
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0%
1/3
0%
1
0%
3
0%
2/3
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0%
0%
2)
0%
0%
If x
2
+ px + q = 0 is the quadratic equation whose rots are a – 2 and b – 2 where a and b are the roots of x
2
– 3x + 1 = 0 then
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p = 1, q = 5
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p = 1, q = –5
0%
p = –1, q = 1
0%
none of these
The value of ‘a’ for which one root of the quadratic equation (a
2
– 5a + 3)x
2
+ (3a – 1)x + 2 = 0 is twice as large as the other is
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0%
0%
2)
0%
0%
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A.P
0%
G.P
0%
H.P
0%
None of these
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