Relation between Roots and Coefficients for Quadratic
If gx=k has...
Question
If g(x)=k has exactly two solutions then k belong to
A
(−2,−1)
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B
(−1,0)
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C
(−3,−2)
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D
None of these
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Solution
The correct option is D None of these Let f(x)=u(x)−2v(x) where u(x)=min(x2,|x|);|x|≤1max(x2,|x|);|x|>1 from the figure Clearly u(x)=x2 v(x)=min(x2,|x|);|x|>1max(x2,|x|);|x|≤1 Clearly, v(x)=|x| and g(x)=minf(t);−3≤t≤x;−3≤x≤0maxf(t);0≤t≤x;0≤x≤3 f(x)=u(x)−2v(x)=x2−2|x| g(x)=min(f(t))=t2−2|t|=t2+2t, if −3<t<x g(x)=x2+2x if x < -1, else g(x)=−1 for x>-1 g(x)=max(f(t))=t2−2|t|=t2−2t, if 0<t<x g(x)=0 if x<2, else g(x)=x2−2x for x>2