Question

if alpha and beta are the zeros of quadratic polynomial f(x)= x square +px+q form a polynomial whose zeros are 1/alpha and 1/beta
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Answer 1

Answer:

in the first case given that α and β are the zeroes of x²+px+q

sum of zeroes = α+β= -b/a                                   {here a =1; b=p; c=q}

                                  = -p/1

                                 = -p-----(1)

product of zeroes = αβ=c/a

                                    = q-----(2)

we need to find a polynomial whose zeros are 1/α and 1/β

sum of zeroes = 1/α+1/β

                         = (β+α)/αβ

                           = -p/q  [ from equation (1) and (2)

product of zeroes = (1/α)(1/β)

                              = 1/αβ= 1/q [from equation 2 ]

now we need to find a polynoial whose sum is -p/q and product is 1/q

sum of zeroes  = -p/q = -b/a

product of zeroes = 1/q = c/a

we can see that a =q; b = p; c= 1

Hence the required polynomial is qx²+px+1.

Another way for doing this @ https://brainly.in/question/9336174