Question

if alpha and beta are the zeroes of polynomial 5x^2-3x-1 then find the value of 1/alpha +1/beta +2

Answer 1

Hello users .....
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We know that:
For a quadratic equation : ax² + bx + c = 0 :

if α and β Are the roots of equation.

sum of roots (α+β) = -b / a 
And
product of roots (αβ) = c / a 

Here,
for given quadratic equation 
5x² - 3x - 1 = 0 

here,
a = 5 , b = -3 and c = -1

Sum of roots (α+β) = -b / a 

=> α+β =  -(-3)/(5) = 3 / 5

And
product of roots (αβ) = c / a 

=> αβ = (-1) / 5 = -1 / 5 

Now,
1 / α + 1 / β = (α+β) / αβ   ( taking LCM )

=> 1 / α + 1 / β = (3/5) / (-1/5)

=> 1 / α + 1 / β = 3 / -1

=> ( 1 / α + 1 / β ) = -3

=> ( 1 / α + 1 / β ) + 2  = -3 + 2 

=> ( 1 / α + 1 / β ) + 2 = -1 Answer 

Hope it helps :)