If the roots of the equation `b x^2+""c x""+""a""=""0` be imaginary, then for all real values of x, the expression `3b^2x^2+""6b c x""+""2c^2` is (1) greater than 4ab (2) less than 4ab (3) greater than `4a b` (4) less than `4a b`

Explanation

`bx^2 + cx + a = 0`

`D< 0`

`c^2 - 4ab < 0`

`c^2 < 4ab`

now, `3b^2x^2 + 6bcx + 2c^2`

minimum value=`-D/(4a)`

`-(36b^2c^2 - 4(3b^2)(2c^2))/(4 * 3b^2)`

`= (24b^2c^2 - 36b^2c^2)/(12b^2) = (-12b^2c^2)/(12b^2)`

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