Thanks for all the unworthy adulation(
) . Actually there is my personal gain from this section. It helps me revise the formulae and concepts. '
Anyway , today's concepts:
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07/10/2002 THEORY OF EQUATIONS
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(1) For a cubic equation ax^3+bx^2+cx+d=o
sum of the roots = - b/a
sum of the product of the roots taken two at a time = c/a
product of the roots = -d/a
(2) For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0
sum of the roots = - b/a
sum of the product of the roots taken three at a time = c/a
sum of the product of the roots taken two at a time = -d/a
product of the roots = e/a
(3) If an equation f(x)= 0 has only odd powers of x and all these have the same sign coefficients or if f(x) = 0 has only odd powers of x and all these have the same sign
coefficients then the equation has no real roots in each case(except for x=0 in the second case.
(4) Besides Complex roots , even irrational roots occur in pairs. Hence if 2+root(3) is a root , then even 2-root(3) is a root .
(All these are very useful in finding number of positive , negative , real ,complex etc roots of an equation )
i bet all will find it useful while revising quant topics.
Linear Mode
