Question

If p and q are the zeroes of the polynomial 3x2 -5x+2 write the polynomial whose zeroes are 1/p and/q

Answer 1

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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Answer 2

Answer:

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