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. less than `(-4ba)`
B. greater than `4ab`
C. less than `4ab`
D. greater than `(-4ab)`

Answer

B

Explanation

Since roots of `bx^(2)+cx+a=0` are imaginary.
`:.c^(20-4ablt0`
`-c^(2)jgt-4ab`…………..i ltbr Let `Ff(x)=3b^(2)x^(2)+6bcx+2c^(2)`
Sicne `3b^(2)gt0`
and `D=(6bc)^(2)-4(3b^(2))(2c^(2))=12b^(2)c^(2)`d
`:.` Minimum value of `f(x)=-D/(4a)=-(12b^(2)c^(2))/(4(3b^(2)))=-c^(2)gt-4ab`