Question

If alpha and beta are the zeros of the polynomial x2-3x+7,find the quadratic polynomial whose zeros are 1 /alpha and 1 /beta

Answer 1

1/alpha +1/ beta=3/7
1/alpha * beta=1/7
The polynomial=x2-3/7 x+1/7

Answer 2

Heya !!






X² - 3X + 7




Here,


A = 1 , B = -3 and C= 7





Sum of zeroes = -B/A



Alpha + Beta = -(-3)




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



And,



Product of zeroes = C/A



Alpha × Beta = 7 -------(2)






Zeroes of the other quadratic polynomial are 1/Alpha and 1/Beta.




Sum of zeroes of the other quadratic polynomial = 1/Alpha + 1/Beta = Beta + Alpha / Alpha × Beta




=> 3/7




And,




Product of zeroes = 1/Alpha × 1/Beta = 1/Alpha × Beta = 1/7




Therefore,



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




=> X² - (3/7)X + 1/7




=> X² - 3X/7 + 1/7



=> 7X² - 3X + 1.