Question

if a polynomial p(x) has zeros 2 and 3, while a polynomial whose zeroes are reciprocal of zeroes of p(x)
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Answer 1

Given : a polynomial p(x) has. zeroes as 2 and 3

To Find : write a polynomial whose zeroes are reciprocals of zeros of p(x)

Solution :

p(x) has. zeroes as 2 and 3

Reciprocal  will be 1/2  and  1/3

polynomial  having zeroes as 1/2 and 1/3

= (x - 1/2)(x - 1/3)

= (2x - 1)(3x - 1) /6

= (6x²  - 5x + 1)/6

x² - 5x/6  + 1/6

or

= 6x²  - 5x + 1    ( multiplying by constant 6)

6x²  - 5x + 1   has zeroes reciprocal of 2 and 3

Another method

Sum of zeroes = 1/2 + 1/3  =   5/6

product of zeroes = 1/6

x² - (5/6)x + 1/6   is the polynomial

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