If p and q are the zeroes of the polynomial 3x2 -5x+2 write the polynomial whose zeroes are 1/p and/q
Answers
required polynomial is 2x² - 5x + 3.
it is given that, p and q are zeroes of polynomial 3x² - 5x + 2.
sum of zeroes = - coefficient of x/coefficient of x²
or, p + q = -(-5)/3 = 5/3 .......(1)
product of zeroes = constant/coefficient of x²
or, pq = 2/3 .......(2)
now we have to find the polynomial zeroes of which are 1/p and 1/q.
sum of zeroes = 1/p + 1/q
= (p + q)/pq
from equations (1) and (2),
= (5/3)/(2/3) = 5/2
and products of zeros = 1/p × 1/q = 1/pq
= 1/(2/3) = 3/2
now polynomial is x² - (sum of zeroes)x + product of zeroes.
= x² - (5/2)x + (3/2)
= (2x² - 5x + 3)/2
hence required polynomial is 2x² - 5x + 3
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