if alpha and beta are the zeros of the polynomial x square minus 3 into X + 1 – then alpha + 1 into beta + 1 is equal to​

Question

if alpha and beta are the zeros of the polynomial x square minus 3 into X + 1 – then alpha + 1 into beta + 1 is equal to​

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Mia 7 months 2021-10-15T20:17:52+00:00 1 Answer 0 views 0

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    2021-10-15T20:19:20+00:00

    Answer:

    Step-by-step explanation:

    Answer:

    c = – 1

    Step-by-step explanation:

    x² – p ( x + 1 ) + c

    ⇒ x² – p x – p + c

    ⇒ x² – p x + ( c – p )

    Comparing with ax² + bx + c, we get :

    a = 1

    b = – p

    c = c – p .

    Given  :

    ( α + 1 )( β + 1 ) = 0

    ⇒ αβ + α + β + 1 = 0

    Note that, sum of roots = – b/a

    α + β = – b / a

    But b = – p

    a = 1

    So α + β = – ( – p ) / 1 = p

    Product of roots = αβ = c / a

    ⇒ αβ = ( c – p )

    Hence write this as :

    αβ + α + β + 1 = 0

    ⇒ c – p + p + 1 = 0

    ⇒ c + 1 = 0

    ⇒ c = -1

    Hence, the value of c is – 1

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