 # WHAT ARE "SYMMETRIC FUNCTIONS OF ROOTS"?

12 years ago

Dear student,

## Symmetric Function in Quadratic Equation

[i.e. if f(a,b) = f(b,a)].

Some of the symmetric functions of a and b are   All symmetric functions of a and b can be expressed in terms of two symmetric functions a+b and ab.

For instance,     All the best.

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Sagar Singh

B.Tech, IIT Delhi

12 years ago

A function of the roots of am equation, which remains unaltered when any two of the roots are interchanged is called Symmetric function of the roots.

If a,b,c are the roots of an equation of degree 3, then we use the following notation.

∑a = a + b + c + d

∑ 1/a =1/a + 1/b + 1/c + 1/d

∑ ab = ab + bc + cd + da + bd + ac
∑ a2 = a2 + b+ c2 + d2

∑ a2b = a2b + b2a + b2c+ c2b+ c2a+ a2c+a2d+a d2 +b2 d+b d2 +c2d+ d2c

∑ a / b = a / b + b /  a + a / c + c / a + a / d + d / a + b / d + d / b + b / c + c / b + c / d +d / c