if alpha and beta are zeroes of the quadratic ploynomial f[x] = ax2 +bx+c then evaluate 1/alpha - 1/beta.

 

Asked by sargu2014477 | 20th Jun, 2018, 08:53: PM

Expert Answer:

The quadratic polynomial ax2 + bx + c = f(x) 
α and β are the zeroes of an equation.
begin mathsize 16px style straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction space and space αβ equals straight c over straight a
1 over straight alpha minus 1 over straight beta equals fraction numerator straight beta minus straight alpha over denominator αβ end fraction equals fraction numerator negative open parentheses straight alpha minus straight beta close parentheses over denominator αβ end fraction..... left parenthesis straight i right parenthesis
Consider comma
open parentheses straight alpha minus straight beta close parentheses squared equals open parentheses straight alpha plus straight beta close parentheses squared plus 4 αβ
open parentheses straight alpha minus straight beta close parentheses squared space equals open parentheses fraction numerator negative straight b over denominator straight a end fraction close parentheses squared plus fraction numerator 4 straight c over denominator straight a end fraction
straight alpha minus straight beta equals square root of straight b squared over straight a squared plus fraction numerator 4 straight c over denominator straight a end fraction end root equals square root of fraction numerator straight b squared plus 4 ac over denominator straight a squared end fraction end root equals fraction numerator square root of straight b squared plus 4 ac end root over denominator straight a end fraction
1 over straight alpha minus 1 over straight beta equals fraction numerator negative open parentheses straight alpha minus straight beta close parentheses over denominator αβ end fraction equals fraction numerator fraction numerator square root of straight b squared plus 4 ac end root over denominator straight a end fraction over denominator straight c over straight a end fraction equals fraction numerator square root of straight b squared plus 4 ac end root over denominator straight c end fraction

space end style

Answered by Sneha shidid | 21st Jun, 2018, 09:36: AM

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