If the equation |x2+bx+c|=k has four real roots, then
A
b2−4c>0 and 0<k<4c−b24
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B
b2−4c<0 and 0<k<4c−b24
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C
b2−4c>0 and k>4c−b24
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D
none of these
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Solution
The correct option is B none of these |x2+bx+c|=k let f(x)=|x2+bx+c| & g(x)=k from the figure: Since, f(x)=0 have real roots Therefore, D=b2−4c>0...(1) maximum value of f(x) occur at x=−ba.
Therefore, max(f(x))=∣∣∣4c−b24∣∣∣=b2−4c4 from the figure it is clear that, f(x) & g(x) will have four point of intersection when 0<g(x)<max(f(x)) ⇒0<k<b2−4c4 Ans: D