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Question

# f(x)=|9âˆ’x2|âˆ’|xâˆ’a| then which of the following statements is/are true?

A
For a = 8, number of distinct real roots of f(x)=0 is 4
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B
For a = 8, number of distinct real roots of f(x)=0 is 3
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C
For a = 3, number of distinct real roots of f(x)=0 is 4
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D
For a = 3, number of distinct real roots of f(x)=0 is 3
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Solution

## The correct options are A For a = 8, number of distinct real roots of f(x)=0 is 4 D For a = 3, number of distinct real roots of f(x)=0 is 3|9−x2|=|x−a| Find extreme cases where |x-a| touches |9−x2|. For Right side 9−x2=−x+a x2−x+a−9=0⇒D=0 1 = 4(a-9) a=374 but for a=3→ three solutions exists. From the figure we can conclude that for aϵ(−374,−3)∪(−3.3)∪(3,374)→4 real roots. For aϵ{−374,−3,3,374}→f(x)=0 has 3 real roots.

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