(C) Given that the equation $bx^2 + cx + a = 0$ has imaginary roots,the discriminant $D < 0$.Therefore,$c^2 - 4ab < 0$,which implies $c^2 < 4ab$.Multi

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(C) Given that the equation $bx^2 + cx + a = 0$ has imaginary roots,the discriminant $D Therefore,$c^2 - 4ab Multiplying by $-1$,we get $-c^2 > -4ab$.Now,consider the expression $E = 3b^2x^2 + 6bcx + 2c^2$.$E = 3(b^2x^2 + 2bcx + c^2) - c^2$.$E = 3(bx + c)^2 - c^2$.Since $(bx + c)^2 \geq 0$,it follows that $3(bx + c)^2 \geq 0$.Thus,$E \geq -c^2$.Since $-c^2 > -4ab$,we have $E > -4ab$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If the roots of the equation $bx^2 + cx + a = 0$ are imaginary,then for all real values of $x,$ the expression $3b^2x^2 + 6bcx + 2c^2$ is :

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A
$> 4ab$
B
$< 4ab$
C
$> -4ab$
D
$< -4ab$

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