If both (x – 2) and (x-1/2 ) are the factors of px^2 + 5x + r, then show that p = r
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Given polynomial = px^2 + 5x + r
Given factors - (x-2) and (x-1/2)
therefore, zeroes of the polynomial are 2 and 1/2
now, sum of the zeroes = 2+1/2 = 5/2
product of zeroes = 2 x 1/2 = 1
from given polynomial, sum of zeroes = -b/a = -5/p
product of zeroes = c/a = r/p
therefore, r/p= 1
r=p
Given factors - (x-2) and (x-1/2)
therefore, zeroes of the polynomial are 2 and 1/2
now, sum of the zeroes = 2+1/2 = 5/2
product of zeroes = 2 x 1/2 = 1
from given polynomial, sum of zeroes = -b/a = -5/p
product of zeroes = c/a = r/p
therefore, r/p= 1
r=p
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