if alpha and beta are the zeros of the polynomial 5x^2 -8x-4 write the value of alpha +beta +alphabeta

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2 thoughts on “if alpha and beta are the zeros of the polynomial 5x^2 -8x-4 write the value of alpha +beta +alphabeta<br /><br />​”

1. Answer:

   For a quadratic equation, ax2+bx+c=0,

   The sum of the roots=a−b and product of the roots is ac

   Here sum of roots= α+β=2−5

   Product of roots=αβ=21

   Therefore,α+β+αβ=2−5+21

   ⇒ α+β+αβ=−2

   Therefore,Option A is correct.

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2. Solution

   Given :–

   • Polynomial, 5x² – 8x – 4 = 0
   • α & β are roots of this Equation.

   Find :–

   • Value of α + β + α β

   Explanation

   Formula

   ★Sum of roots = –(coefficient of x)/(coefficient of x²)

   ★Product of roots = (constant part)/+coefficient of x²)

   So, Now

   ==> Sum of roots = -(-8)/5

   ==> α + β = 8/5 ______________(1)

   and,

   ==> Product of roots = (-4)/5

   ==> α β = -4/5________________(2)

   Now , add Equation (1) & Equation (2)

   ==> α + β + α β = 8/5 – 4/5

   ==> α + β + α β = (8 – 4)/5

   ==> α + β + α β = 4/5

   Hence

   • Value of α + β + α β will be = 4/5

   __________________

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