Question

if alpha and beta are the zeroes of the polynomial 2x²+7x-3 , find the value of following : (i) 1/alpha+1/beta​

Answer 1

Answer:

1/alpha + 1/beta = 1/α + 1/β = 7/3

Step-by-step explanation:

Given : zeroes of the polynomial 2x²+7x-3 is α (alpha) and β (beta).

Here,  a(coefficient of x²) = 2

         b(coefficient of x) = 7

          c(constant term) = - 3

Sum of zeroes of the polynomial = - (coefficient of x) / (coefficient of x²)

                                            α + β  = - b/a

                                            α + β  = - (7) / 2

                                            α + β  = - 7/2   —————————— (i)  

Product of zeroes of the polynomial = (constant term) / (coefficient of x²)

                                            α × β  =  c/a

                                              αβ    = - (3) / 2

                                              αβ    = - 3/2   —————————— (iI)  

   1/α + 1/β = (α + β) / (αβ)    

   1/α + 1/β = (-7/2) / ( -3/2)    —————————— from (i) and (ii)

∴  1/α + 1/β = 7/3