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(C) Given that the quadratic equation $bx^2 + cx + a = 0$ has imaginary roots,its discriminant must be less than zero.Therefore,$D = c^2 - 4ab < 0$,wh

Vedclass · Accepted Answer

$> -4ab$

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(C) Given that the quadratic equation $bx^2 + cx + a = 0$ has imaginary roots,its discriminant must be less than zero.Therefore,$D = c^2 - 4ab Multiplying by $-1$,we get $-c^2 > -4ab$.Now,consider the expression $E = 3b^2x^2 + 6bcx + 2c^2$.We can rewrite this as $E = 3(b^2x^2 + 2bcx + c^2) - c^2$.This simplifies to $E = 3(bx + c)^2 - c^2$.Since $(bx + c)^2 \geq 0$ for all real $x$,it follows that $3(bx + c)^2 \geq 0$.Therefore,$E = 3(bx + c)^2 - c^2 \geq -c^2$.Since we established that $-c^2 > -4ab$,it follows that $E > -4ab$.

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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