Sum of the product of the roots taken two at a time
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let the polynomial be axⁿ+bxⁿ⁻¹......+mx²+ox+p (note n is not coefficient)
whose roots are α,β,γ,....ρ (n roots)
then,
xⁿ+(b/a)xⁿ⁻¹......+(m/a)x²+(o/a)x+(p/a) = (x-α)(x-β)(x-γ)....(x-ρ)
= xⁿ + (∑α)xⁿ⁻¹.....+
sum of product of 2 roots= c/a = (coefficeint of xⁿ⁻²)/(coefficeint of xⁿ)
whose roots are α,β,γ,....ρ (n roots)
then,
xⁿ+(b/a)xⁿ⁻¹......+(m/a)x²+(o/a)x+(p/a) = (x-α)(x-β)(x-γ)....(x-ρ)
= xⁿ + (∑α)xⁿ⁻¹.....+
sum of product of 2 roots= c/a = (coefficeint of xⁿ⁻²)/(coefficeint of xⁿ)
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