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The number of distinct real roots of x^...

The number of distinct real roots of ` x^4 - 4 x^3 + 12 x^2 + x - 1 = 0` is :

Text Solution

Verified by Experts

The correct Answer is:
a
Let `(x)=x^(4)-4x^(3)+12x^(2)+x-1`
`:.f'(x)=4x^(3)-12x^(2)+24x+1`
`impliesf''(x)=12x^(2)-24x+24`
`=12(x^(2)-2x+2)`
`=12[(x-1)^(2)+1]gt0`
i.e. `f"(x)` has no real roots.
Hence `f(x)` has maximum two distinct real roots, where `f(0)=-1`.
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