Question

If alpha , beta are the two zeroes of the polynomial 25p²-15p+2 , find a quadratic polynomial whose zeroes are 1/2alpha and 1/2beta.

Answer 1

Given that : Alpha and Beta are zeroes of polynomial 25P² - 15P + 2 .


Therefore,


Sum of zeroes = -b/a


Alpha + Beta = 15/25.


And,


Product of zeroes = c/a


Alpha × Beta = 2/25.



Let , S = 1/2alpha + 1/2beta = 1/2 × (@+ß)/(@×ß)




=> 1/2 × 15/25/2/25


=> 1/2 × 15/2


=> 15/4.



P = 1/2alpha × 1/2beta = 1/4alhabeta = 1/4×2/25



=> 25/8.



Therefore,


Required quadratic polynomial = P²-(S)P + P


=> P² - 15p/4 + 25/8.


=> 8P² - 30P + 25.

Answer 2

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