Let f(x) = x^2 + ax + bcosx, a being an integer and b is a real number The - Maths - Relations and Functions

Question

Let f(x) = x^2 + ax + bcosx, a being an integer and b is a real
number The number of ordered pairs (a,b) for which the equation
f(x)=0 and f(f(x))=0 have the same (non empty) set of real roots is
:

Ghanshyam Dhakar · Accepted Answer

Dear student,
fx = x2+ax+bcosx  fx = 0x2+ax+bcosx =0  
1 ffx  =0fx 2+afx +bcosfx =0 
2for  fx = 0 and ffx  =0 have same root then use  fx = 0 in eq2 fx 2+afx +bcosfx =00+0+bcos0 =0b×1 = 0then b=0 use eq1x2+ax+bcosx =0x2+ax =0xx+a=0for non empty solutionx+a=0x=-afor fixed value of b The number of ordered pairs of (a,b) =1
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Let f(x) = x^2 + ax + bcosx, a being an integer and b is a real number. The number of ordered pairs (a,b) for which the equation f(x)=0 and f(f(x))=0 have the same (non empty) set of real roots is :