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Suppose f(x) is a polynomial of degree four, having critical points at -1,0,1. If T=\left \{ x\; \epsilon \; R\; \right | \right f(x)=f(0)\}, then the sum of squares of all the elements of T  is :
Option: 1 4
Option: 2 6
Option: 3 2
Option: 4 8
 

Answers (1)

best_answer

\\f^{\prime}(x)=x(x+1)(x-1)=x^{3}-x \\ \int d f(x)=\int x^{3}-x d x \\ f(x)=\frac{x^{4}}{4}-\frac{x^{2}}{2}+C \\ f(x)=f(0) \\ \frac{x^{4}}{4}-\frac{x^{2}}{2}=0

\\x^{2}\left(x^{2}-2\right)=0 \\ x=0,0, \sqrt{2},-\sqrt{2} \\ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=0+2+2=4

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