Question

tsquare-p(t+1)-c find (alfa+1)( beta +1)

Answer 1

Complete question is

If α and β be the zeroes of

       t² - p (t + 1) - c,

then find (α + 1) (β + 1)

Answer :

    (α + 1) (β + 1) = - c + 1

Solution :

The given polynomial is

  P(t) = t² - p (t + 1) - c

         = t² - pt - (p + c)

If α and β be the zeroes of P(t), by the relation between zeroes and coefficients, we get

  α + β = - ( - p)/1 = p .....(i)

  αβ = - (p + c) .....(ii)

Now, (α + 1) (β + 1)

      = αβ + (α + β) + 1

      = - (p + c) + p + 1

      = - p - c + p + 1

      = - c + 1