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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 a. `b^2-4c > 0` and `0 < k < (4c-b^2)/4` b. `b^2-4c < 0` and `0 < k < (4c-b^2)/4` c. `b^2-4c > 0` and `k > (4c-b^2)/4` d. none of these

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To solve the problem, we need to analyze the equation \( |x^2 + bx + c| = k \) and determine the conditions under which it has four real roots. ### Step 1: Understanding the Equation The equation \( |x^2 + bx + c| = k \) implies that the expression \( x^2 + bx + c \) can either equal \( k \) or \( -k \). Therefore, we can break this down into two separate equations: 1. \( x^2 + bx + c = k \) 2. \( x^2 + bx + c = -k \) ### Step 2: Finding Roots of Each Equation ...
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