Q1) if alpha and beta are zeroes of the quadratic polynomial f(x)=3x²-5x-2, then evaluate alpha³+beta³
Q2) if one of the zeroes of the cubic polynomial x³+ax²+bx-c is -1, then find the product of other two zeroes? (Plz help because its answer us given c of Q2)

Asked by mkmishra101 | 11th Jun, 2016, 03:35: PM

Expert Answer:

begin mathsize 12px style 1. space I f space alpha space a n d space beta space a r e space r o o t s space o f space t h e space q u a d r a t i c space p o l y n o m i a l space 3 x squared minus 5 x minus 2 comma space t h e n
alpha plus beta equals negative fraction numerator open parentheses negative 5 close parentheses over denominator 3 end fraction equals 5 over 3
alpha beta equals fraction numerator negative 2 over denominator 3 end fraction equals negative 2 over 3
alpha cubed plus beta cubed equals open parentheses alpha plus beta close parentheses cubed minus 3 alpha beta open parentheses alpha plus beta close parentheses
rightwards double arrow alpha cubed plus beta cubed equals open parentheses 5 over 3 close parentheses cubed minus 3 open parentheses negative 2 over 3 close parentheses open parentheses 5 over 3 close parentheses
rightwards double arrow alpha cubed plus beta cubed equals 125 over 27 plus 10 over 3
rightwards double arrow alpha cubed plus beta cubed equals fraction numerator 125 plus 90 over denominator 27 end fraction equals 215 over 27

2. space
F o r space x cubed plus a x squared plus b x minus c comma space
p r o d u c t space o f space a l l space r o o t s equals negative fraction numerator c o n s tan t space t e r m over denominator c o e f f i c i e n t space o f space x cubed end fraction equals negative fraction numerator negative c over denominator 1 end fraction equals c
G i v e n space t h a t space o n e space r o o t space i s space minus 1.
S o space open parentheses negative 1 close parentheses open parentheses p r o d u c t space o f space o t h e r space t w o space z e r o e s close parentheses equals c
rightwards double arrow P r o d u c t space o f space o t h e r space t w o space z e r o e s space i s space minus c end style

Answered by satyajit samal | 13th Jun, 2016, 09:35: AM

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