Quirky equation V

Algebra Level 3

x 4 − 9 x 3 + 27 x 2 − 30 x + 8 = 0 x^4-9x^3+27x^2-30x+8=0 Find the sum of all values of x x satisfying the above equation.


The answer is 9.

Rohit Udaiwal by Rohit Udaiwal , 20, India

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1 solution

Akshat Sharda
Nov 21, 2015

Let the roots of x 4 − 9 x 3 + 27 x 2 − 30 x + 8 = 0 x^4-9x^3+27x^2-30x+8=0 be x 1 x_{1} , x 2 x_{2} , x 3 x_{3} and x 4 x_{4} .

By Vieta's Formula :

∑ i = 1 4 x i = − b a = − ( − 9 ) 1 = 9 \displaystyle \sum^{4}_{i=1}x_{i}=-\frac{b}{a}=-\frac{(-9)}{1}=9

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