If the equation `|x^2+bx+c|=k` has four real roots, then

Options

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

Answer

1

Explanation

For the equation to have four real roots, the line y = k must
intersect ` y = |x^(2) = bx + c|` at four point.
`therefore D gt 0 and k in (0 , (-D)/(4))`