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If the equation |x^2+b x+c|=k has four r...

If the equation `|x^2+b x+c|=k` has four real roots, then `b^2-4c >0a n d00a n dk >(4c-b^2)/4` none of these

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

Text Solution

Verified by Experts

The correct Answer is:
1

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))`
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