Question

alpha and beta are zeros of polynomial 2 x square - 4 x + 5 from the polynomial where
zero are:1 upon alpha and 1 upon
beta ​

Answer 1

Let p(x) = t² -t -4

On comparing with ax²+bx+c

a= 1, b= -1 , c= -4

Given, α and β are the zeroes of p(x).

Sum of zeroes (α+ β) = -b/a

α+ β = - (-1)/1

α+ β = 1………………..(1)

Product of zeroes (α. β) = c/a

α. β = -4/1= -4

Given, zeroes are 1/α and 1/β .

Sum of zeroes= (1/α+ 1/β) =( α+ β )/α β

Sum of zeroes= 1/ -4= -1/4

[From equation 1]

Product of zeroes= 1/α. 1/β = 1/(α.β)

= 1/-4= -¼

[From equation 2]

Required Polynomial= t²-(Sum of zeroes)t +( Product of zeroes)

= t² -(-1/4)t + (-¼)

= t² + t/4 -¼

= 4t² +t -1

Hence,the Required Polynomial is 4t² +t -1

HOPE THIS WILL HELP YOU....

Answer 2

Answer:

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