Question

if the a and B are the zeros of the quadratic polynomial f( x) = x^2 - x- 2 , find a polynomial where zeroes are 2a+ 1 and 2B+1?​

Answer 1

Answer:

→ Hey Mate,

→ Given question : if the a and B are the zeros of the quadratic polynomial f( x) = x^2 - x- 2 , find a polynomial where zeroes are 2a+ 1 and 2B+1?​

→ Step-by-step explanation:

→ solution :

→ f ( x )  =  x² - x -2

→ a = 1 , b = -1 ,  c = -2

→ a+B = -b / a    ,   a.b = c/a

→ - ( -1 ) / 1                   =  -2 / 1 = -2

→ 1

→ Sum of roots = 2a + 1 + 2B + 1

→                       =  2 (  a + B) + 2

→                       = 2 × 1 + 2

→                      =  4

→  Product of roots = (2a + 1) ( 2B + 1)

→                               =  4aB +  2a + 2B + 1

→                               =   4 × -2 + 2 ( 1 ) + 1

→                               =  -8 + 2 +1 = -5

→  Now , p ( x ) = x² -  ( a +B ) x + aB

→                       = x² - 4x + (-5)

→                      =   x^2 - 4x-5

→    ------------------------------------------------------------------------------------------------