Find the zeros of the polynomial 21x squared-3 and verify the relationship between the zeros and the coefficients.

Asked by priyaherkar500 | 19th Jun, 2014, 06:40: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space p o l y n o m i a l space 21 x squared minus 3. W e space n e e d space t o space f i n d space t h e space z e r o s space o f space t h e space p o l y n o m i a l comma space space 21 x squared minus 3 rightwards double arrow space 21 x squared minus 3 equals 0 rightwards double arrow 3 open parentheses space 7 x squared minus 1 close parentheses equals 0 rightwards double arrow 7 x squared minus 1 equals 0 rightwards double arrow 7 x squared equals 1 rightwards double arrow x squared equals 1 over 7 rightwards double arrow x equals plus-or-minus fraction numerator 1 over denominator square root of 7 end fraction S u m space o f space t h e space r o o t s space equals space fraction numerator minus b over denominator a end fraction equals 0 over 21 equals 0 P r o d u c t space o f space t h e space r o o t s space equals space c over a equals fraction numerator minus 3 over denominator 21 end fraction equals fraction numerator minus 1 over denominator 7 end fraction S i n c e space fraction numerator 1 over denominator square root of 7 end fraction space a n d space minus fraction numerator 1 over denominator square root of 7 end fraction space a r e space t h e space r o o t s comma space s u m space o f space t h e space r o o t s space equals space fraction numerator 1 over denominator square root of 7 end fraction minus fraction numerator 1 over denominator square root of 7 end fraction equals 0 A n d space t h e space p r o d u c t space o f space t h e space r o o t s space equals open parentheses fraction numerator 1 over denominator square root of 7 end fraction close parentheses open parentheses minus fraction numerator 1 over denominator square root of 7 end fraction close parentheses equals fraction numerator minus 1 over denominator 7 end fraction H e n c e space i t space i s space p r o v e d.

Answered by Vimala Ramamurthy | 20th Jun, 2014, 10:44: AM