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`

Options

A. greater than 4 ab
B. less than 4 ab
C. greater than -4ab
D. less than -4ab

Answer

C

Explanation

It is given that the roots of `bx^(2) + cx + a = 0` are imaginary.
`therefore" "c^(2)-4ab lt 0 rArr c^(2) lt 4ab`
Let `y = 3b^(2)x^(2) + 6bcx + 2c^(2)`. Clearly, it represents a parabola opening upward. So,
`y_(min)=-(36b^(2)c^(2) - 24b^(2)c^(2))/(12b^(2))= 0 c^(2) gt - 4ab`