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CBSE Class 10 Answered

If m and n are zeroes of the polynomial 3x^2 + 11x – 4, find the value of m/n + n/m
Asked by Marie | 01 Feb, 2020, 05:20: PM
Expert Answer
m and n are zeroes of the polynomial 3x2 + 11x – 4, the value of m/n + n/m is
a = 3, b = 11, c = -4
m + n = -b/a = -11/3
mn = c/a = -4/3
begin mathsize 16px style straight m over straight n plus straight n over straight m equals fraction numerator straight m squared plus straight n squared over denominator mn end fraction end style
size 16px equals fraction numerator begin mathsize 16px style left parenthesis straight m plus straight n right parenthesis end style to the power of size 16px 2 size 16px minus size 16px 2 size 16px mn over denominator size 16px mn end fraction
size 16px equals fraction numerator begin mathsize 16px display style left parenthesis fraction numerator negative 11 over denominator 3 end fraction right parenthesis squared minus 2 cross times left parenthesis fraction numerator negative 4 over denominator 3 end fraction right parenthesis end style over denominator fraction numerator size 16px minus size 16px 4 over denominator size 16px 3 end fraction end fraction
size 16px equals fraction numerator begin mathsize 16px display style 121 over 9 plus 8 over 3 end style over denominator fraction numerator size 16px minus size 16px 4 over denominator size 16px 3 end fraction end fraction
size 16px equals fraction numerator size 16px 121 size 16px plus size 16px 24 over denominator size 16px 9 end fraction size 16px cross times fraction numerator size 16px minus size 16px 3 over denominator size 16px 4 end fraction size 16px equals fraction numerator size 16px minus size 16px 145 over denominator size 16px 12 end fraction
 

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