Question

if alpha and beta are the zeros of the quadratic polynomial x square - p[x-1]-C ,show that [alpha -1] [beta +1]= 1-C​

Answer 1

Correct question : ( α - 1 )( β - 1 ) = 1 - C.

Answer:

1 - C

Step-by-step explanation:

Given polynomial : x^2 - p( x - 1 ) - C

⇒ x^2 - p( x - 1 ) - C

⇒ x^2 - px + p - C

⇒ x^2 - px + ( p - C )

  We know,

         quadratic polynomials / equations represent sum and product of their roots as S and P in the equation in form of x^2 - Sx + P = 0.

 Therefore, here, in polynomial x^2 - px + ( p - C )

    Sum of roots = p

   Product of roots = ( p - C )

Here,

⇒ ( α - 1 )( β - 1 )

⇒ αβ - α - β + 1

⇒ αβ - ( α + β ) + 1

⇒ ( product of roots ) - ( sum of roots ) + 1

⇒ ( p - C ) - p + 1

⇒ p - C - p + 1

⇒ - C + 1

⇒ 1 - C

             Proved.