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Question

f(x)=|9x2||xa| 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
|9x2|=|xa|

Find extreme cases where |x-a| touches |9x2|.
For Right side 9x2=x+a
x2x+a9=0D=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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