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If the roots of the quadratic equation ax2+bx+c=0 are imaginary, then for all real values of x, the minimum value of the expression 3a2x2+6abx+2b2 is

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Important Questions on Theory of Equations

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If the roots of equation x2-2cx+ab=0 are real and unequal, then the roots of x2-2a+bx+a2+b2+2c2=0 are
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If fx=x2+ax+2=0 and gx=x2+2x+a=0 have only one real common root, then sum of the roots of fx+gx=0 is
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Assertion A: 3x2-16x+4>-16 is satisfied for some values of real x in 0,103

Reason R: ax2+bx+c and a will have the same sign for some values of xR when b2-4ac>0

The correct option among the following is

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fx=ax2-bx-a is a quadratic expression. If K is the least real number such that fxK,  xR, then
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The smallest negative integer satisfying both the quadratic inequalities x2<4x+77 and x2>4 is
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If x2-5x-14>0x lie outside [α, β], then αβ=
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If y=x2+14x+9x2+2x+3x, then the interval of maximum length in which y lies is
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If the roots of the equation x2+x+a=0 exceed a, then