Question

If α and β are the zeros of a quadratic polynomial f(x) =x² - 3 x - 2 , find a quadratic polynomial whose zeros are β/α and α/β .

Answer 1

Heya !!!




P(X) = X² - 3X - 2




Here,



A = 1 , B = -3 and C = -2




Sum of zeroes = -B/A




Alpha + Beta = -(-3)/1




Alpha + Beta = 3 ----------(1)



And,



Product of zeroes = C /A



Alpha × Beta = -2 ---------(2)






Sum of the zeroes quadratic polynomial whose zereos are Beta/Alpha and Alpha / Beta





Sum of zeroes = ( Beta / Alpha + Alpha / Beta)




=> ( Alpha + Beta ) / ( Alpha × Beta)





=> -3/2




And,


Product of zeroes = ( Beta / Alpha × Alpha / Beta )



=> ( Beta × Alpha ) /. ( Alpha × Beta )




=> -2/-2 = 1




Therefore,



Required quadratic polynomial = X²-(Sum of zeroes )X + Product of zeroes




=> X² - (-3/2)X + 1




=> X² + 3X/2 +1




=> 2X² + 3X + 2





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