Question

1. If a and B are the zeros of the quadratic polynomial f(x) = x2 - 2x + 3, find a
polynomial whose roots are (i) a + 2,b+2 (2) a-1/a+1 , b-1/b-1​

Answer 1

ii) It is given that a and b are zeroes of polynomial

f(x) = x2 - 2x + 3.

Therefore, a + b = 2

ab = 3

Now, the zeroes of the required quadratic polynomial are a - 1/a + 1 and b - 1/b + 1

Sum of roots =

a - 1/a + 1 + b - 1/b + 1= ab+a-b-1+ab-a+b-1/(a+1)(b+1)

=2ab-2/ab+a+b+1

= 6-2/3+2+1

= 4/6

=2/3

Similarly, we get product of roots = 1/3

Now, the required polynomial is given by:

x2 -(Sum of roots)x + (Product of roots)

i.e., x2 - (2/3)x + (1/3)

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