MathematicsIf α   and β   are the zeroes of the polynomial 3 x 2 +5x+2  , find the value of 1 α + 1 β  .

If α   and β   are the zeroes of the polynomial 3 x 2 +5x+2  , find the value of 1 α + 1 β  .


  1. A
    4 2  
  2. B
    3 2  
  3. C
    5 2  
  4. D
    1 2   

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    Solution:

    Given that a polynomial 3 x 2 +5x+2  .
    We have to find the value of  1 α + 1 β  .
    Let p x =3 x 2 +5x+2   and assume α   and β   to be the zeroes of the polynomial p(x), then write the sum of the zeroes.
    We know the sum of zeroes of a quadratic polynomial is Coefficient of x Coefficient of  x 2   and the product of zeroes is Constant term Coefficient of  x 2 .  
    So,
    Coefficient of x Coefficient of  x 2 =α+β Coefficient of x Coefficient of  x 2 = 5 3  
    Write the product of the zeroes.
    Constant term Coefficient of  x 2 =αβ Constant term Coefficient of  x 2 = 2 3  
    Use the sum and product of zeroes to write the value of 1 α + 1 β  .
    1 α + 1 β = α+β αβ 1 α + 1 β = 5 3 2 3 1 α + 1 β = 5 2  
    Hence, the value equal to 1 α + 1 β   is 5 2  .
    Therefore, option (3) is correct.
     
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