Suppose f(x) is a polynomial of degree four, having critical points at -1,0,1. If T = {x ∈ R | f(x) = f(0)}, then the sum of squares of all the elements of T is:
Suppose f(x) is a polynomial of degree four, having critical points at -1,0,1. If T = {x ∈ R | f(x) = f(0)}, then the sum of squares of all the elements of T is:
Option 1 -
8
Option 2 -
6
Option 3 -
2
Option 4 -
4
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:f' (x) = k*x (x+1) (x-1) = k (x³-x)
=> f (x) = k (x? /4 - x²/2) + C
=> f (0) = C
=> f (x) = f (0)
=> k (x? -2x²)/4 + C = C
=> x² (x²-2)=0
=> x = {0, √2, -√2}
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