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Let f(x)=|[1,1,1] , [3-x,5-3x^2,3x^3-1] ...

Let `f(x)=|[1,1,1] , [3-x,5-3x^2,3x^3-1] , [2x^2-1,3x^5-1,7x^8-1]|` then the equation of `f(x)=0` has

A

f(x) = 0 has at least two real roots

B

f'(x) =0 has at least one real root.

C

f(x) is many-one function

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`f(x)=|(1,1,1),(3-x,5-3x^(2),3x^(3)-1),(2x^(2)-1,3x^(5)-1, 7x^(8)-1)|`
Clearly `f(0)=f(1)=0`
Hence, `f(x)=0` atleast two real roots.
Also for atleast one `x in (0,1),f'(x)=0` (Rolle's theorem)
Obviously function is many-one.
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