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Q.

If f(x)=x    a    aa    x    aa    a    x=0, then which of the following is correct ?

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a

f'(x) = 0 and f"(x) = 0 has one common root

b

f(x) = 0 and f'(x) = 0 has one common root

c

sum of roots of f(x) = 0 is -3a

d

none of these

answer is B.

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Detailed Solution

Applying C1→C1+C2+C3, we getΔ=x+2a    a    ax+2a    x    ax+2a    a    x=(x+2a)1aa1xa1axApplying R1→R1−R2 and R2→R2−R3, we getΔ=(x+2a)0a−x00x−aa−x1ax=(x−a)2(x+2a)    roots are a,a,-2a
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