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WHAT ARE "SYMMETRIC FUNCTIONS OF ROOTS"?

WHAT ARE "SYMMETRIC FUNCTIONS OF ROOTS"?

Grade:12

2 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 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,

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Aiswarya Ram Gupta
35 Points
10 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

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