The equation ` x^(2) + ax+b^2=0` has two roots each of which exceeds a number c, then :

Options

A. `a^(2) lt 4b^(2)`
B. `c^(2) + ac + b^(2) gt 0`
C. `-a//2 lt c`
D. none of these

Answer

B

Explanation

Let `f(x) = x^(2) + ax + b^(2)`.
Clearly, y = f(x) represents a parabola opening upward.
If both roots are greater than c, then c is less than both the roots which are real.
`therefore" "f(c) gt 0, "Disc" gt 0 and c lt -(a)/(2)`
`rArr" "c^(2) + ac + b^(2) gt 0, a^(2) - 4b^(2) ge 0 and c lt -(a)/(2)`
`rArr" "c^(2) + ac + b^(2) gt 0, a^(2) ge 4b^(2) and c lt -(a)/(2)`