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CBSE Class 10 Answered

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Asked by ysiddharth83 | 31 Mar, 2020, 03:09: PM
answered-by-expert Expert Answer
If alpha and beta are the zeroes of the quadratic polynomial ax2+bx+c then evaluate a(alpha2/beta + beta2/alpha)+b(alpha/beta+beta/alpha)
alpha space a n d space beta space a r e space t h e space z e r o e s space o f space t h e space p o l y n o m i a l space P left parenthesis x right parenthesis equals a x squared plus b x plus c rightwards double arrow alpha plus beta equals negative b over a space space a n d space space alpha beta equals c over a C o n s i d e r comma a open parentheses alpha squared over beta plus beta squared over alpha close parentheses plus b open parentheses alpha over beta plus beta over alpha close parentheses equals a open parentheses fraction numerator alpha cubed plus beta cubed over denominator alpha beta end fraction close parentheses plus b open parentheses fraction numerator alpha squared plus beta squared over denominator alpha beta end fraction close parentheses equals a open parentheses fraction numerator open parentheses alpha plus beta close parentheses open parentheses alpha squared plus beta squared minus alpha beta close parentheses over denominator alpha beta end fraction close parentheses plus b open parentheses fraction numerator open parentheses alpha plus beta close parentheses squared minus 2 alpha beta over denominator alpha beta end fraction close parentheses equals a open parentheses fraction numerator negative b over a cross times open square brackets open parentheses alpha plus beta close parentheses squared minus 3 alpha beta close square brackets over denominator c over a end fraction close parentheses plus b open parentheses fraction numerator begin display style b squared over a squared end style minus 2 begin display style c over a end style over denominator begin display style c over a end style end fraction close parentheses equals a open parentheses fraction numerator negative b over a cross times open square brackets begin display style b squared over a squared end style minus 3 begin display style c over a end style close square brackets over denominator c over a end fraction close parentheses plus b open parentheses fraction numerator begin display style b squared over a squared minus 2 c over a end style over denominator begin display style c over a end style end fraction close parentheses equals a squared over c open parentheses negative b over a open square brackets fraction numerator b squared minus 3 a c over denominator a squared end fraction close square brackets close parentheses plus fraction numerator a b over denominator c end fraction open parentheses fraction numerator b squared minus 2 a c over denominator a squared end fraction close parentheses equals fraction numerator negative b over denominator a c end fraction open parentheses b squared minus 3 a c close parentheses plus fraction numerator b over denominator a c end fraction open parentheses b squared minus 2 a c close parentheses equals fraction numerator b over denominator a c end fraction open parentheses a c close parentheses equals b
Answered by Renu Varma | 31 Mar, 2020, 05:41: PM

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