JEE Main2009MathematicsQuadratic EquationActual

If the roots of the equation b x^2+c x+a=0 be imaginary, then for all real values of x , the expression 3 b^2 x^2+6 b c x+2 c^2 is

Options

Agreater than 4 a b
Bless than 4 a b
Cgreater than -4 a b
Dless than - 4ab

Correct answer

C. greater than -4 a b

Step-by-step solution

b x^2+c x+a=0 Roots are imaginary c^2-4 a b -4 a b3 b^2 x^2+6 b c x+2 c^2 since 3 b^2>0 Given expression has minimum value Minimum value = 4 (3 b^2 ) (2 c^2 )-36 b^2 c^2 4 (3 b^2 ) =- 12 b^2 c^2 12 b^2 =-c^2>-4 a b .

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