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Asked by origami & craft | 26 Mar, 2019, 11:45: AM
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if α, β and γ are roots of cubic polynomial  ax3 +bx2 +cx +d = 0
 
then α+β+γ = - b/a,  αβ +βγ +γα = c/a   and   αβγ = -d/a
 
Given cubic polynomial : 2x3 +7x2 -x +13 = 0
 
hence  α+β+γ = -7/2  ,   αβ +βγ +γα = -1/2,   αβγ = -13/2
 
begin mathsize 12px style 1 over alpha plus 1 over beta plus 1 over gamma space equals space fraction numerator alpha beta space plus space beta gamma space plus space gamma alpha over denominator alpha beta gamma end fraction space equals space fraction numerator begin display style bevelled fraction numerator negative 1 over denominator 2 end fraction end style over denominator begin display style bevelled fraction numerator negative 13 over denominator 2 end fraction end style end fraction space equals space 1 over 13 end style
begin mathsize 12px style alpha squared space plus space space beta squared space plus space gamma squared space plus 2 alpha beta space plus 2 beta gamma space plus 2 gamma alpha space minus space 4 alpha beta gamma space equals space open parentheses alpha space plus space beta space plus gamma close parentheses squared space minus space 4 alpha beta gamma space equals space open parentheses negative 7 over 2 close parentheses squared space minus 4 open parentheses negative 13 over 2 close parentheses space equals space 49 over 4 plus 26 space equals 153 over 4 end style
Answered by Thiyagarajan K | 26 Mar, 2019, 12:39: PM

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