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If the roots of the quadratic equation are imaginary, then for all real values of , the minimum value of the expression is
(a)
(b)
(c)
(d)

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Important Questions on Theory of Equations
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If the roots of equation are real and unequal, then the roots of are

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If and have only one real common root, then sum of the roots of is

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Assertion is satisfied for some values of real in .
Reason and will have the same sign for some values of when .
The correct option among the following is

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is a quadratic expression. If is the least real number such that then

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The smallest negative integer satisfying both the quadratic inequalities and is

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If lie outside then

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If then the interval of maximum length in which lies is

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If the roots of the equation exceed , then
