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Q.

If f(x)=x2+x+34 and g(x)=x2+ax+1 be two real  functions, then the range of a for which g(f(x))=0 has no  real solution is

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a

(−∞,−2)

b

(−2,2)

c

(−2,∞)

d

(2,∞)

answer is C.

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Detailed Solution

f(x)=x2+x+34=x+122+12≥12g(f(x))=f(x)2+af(x)+1 for g(f(x))=0a=−f(x)+1f(x)≤−2
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If f(x)=x2+x+34 and g(x)=x2+ax+1 be two real  functions, then the range of a for which g(f(x))=0 has no  real solution is