Page 18 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

21. .TQhueaodryraotficQEuqaudaratitoicnsEquations eeLleeaarrnn..Ppuunnjjaabb

= 1 + 8 + 6 = 15
The expression a3 + b3 + 3ab represents a symmetric function of a
and b.

2.4.2. Evaluate a symmetric function of roots of a quadratic
equation in terms of its co-efficients

If a, b are the roots of the quadratic equation
ax2 + bx + c = 0, (a m 0) (i)

The functions given in equations (ii) and (iii) are the symmetric
functions for the quadratic equation (i).
Some more symmetric functions of two variables a, b are given
below:

Example 1: If a, b are the roots of the quadratic equation
px2 + qx + r = 0 , (p m 0)
then evaluate a2b + ab2

Solution: Since a, b are the roots of px2 + qx + r = 0, therefore,

Version 1.1 Example 2: If a, b are the roots of the equation 2x2 + 3x + 4 = 0, then
find the value of (i) a2 + b2 (ii)

Solution: Since a, b are the roots of the equation 2x2 + 3x + 4 = 0,
therefore,

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