Question

if alpha and 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

Hello,

P(X) => 25P²-15P+2

Here,

A = 25 , B = -15 and C = 2

Sum of zeroes = -B/A


Alpah + Beta = -(-15)/25


Alpha + Beta = 15/25


And,


Product of zeroes = C/A



Alpha × Beta = 2/25


Sum of Zeroes of Quadratic polynomial whose zeroes are 1/2 ×Alpha and 1/2Beta



Sum of zeroes = 1/2Alpha + 1/2Beta


=> 1/2 × (Alpha + Beta)/(Alpha × Beta)


=> 1/2 × (15/25)/(2/25) = 1/2 × 15/2 = 15/4


And,


Product of zeroes = 1/ 2 Alpha × 1/2 beta = 1/4 Alpna × Beta = 1/ 4 × 2/25



=> 25/8

Therefore,




Required Quadratic polynomial = X²-(Alpha + Beta)X + Alpha × Beta



=> X² - 15/4 X + 25/8


=> X²-15X/4 + 25/8



=> 8X²-30P+25




HOPE IT WILL HELP YOU....... :-)

Answer 2

Here is your answer user.