Question

If a and B are the zeros of the quadratic polynomial p (x)= x^2+x+2,find a polynomial whose zeros are 2a-1 and 2B-1​

Answer 1

Answer:

If α & β are zeros of polynomial f(x) =x²-x-2, how do you find polynomials whose zeros are 2α+1,2β+1?

Two Methods:

If α & β are zeroes of f(x) =x²-x-2

then

α + β = -b/a = 1

α β = c/a = -2

let α’ =2α+1 & β’ = 2β+1

α’ + β’ = 2α+1 + 2β+1

=2α+2β+2 =2(α+β)+2 =2(1)+2=4

α’ β’=(2α+1)(2β+1) = 4α β+2α+ 2β+1 = 4(-2)+2(1)+1=-8+2+1=-5

Polynomial having α’ & β’ as zeroes is given by

k (x²-(α’ + β’)x +α’ β’)

= k (x² - 4x -5) Answer

By giving different values to k, there can be infinite polynomials