Question

If alpha, beta are the zeros of the polynomial f (x) =x^2-3x+2,then find 1/alpha+1/beta​

Answer 1

Answer:

• $\tt{\alpha + \beta = \frac{-b}{c} = 3}$

• $\tt{\alpha \beta = \frac{c}{a} = 2}$

$\tt{\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta}}$

=> $\tt{\frac{3}{2}}$

______________

Answer 2

Given

α and β are the zeroes of the polynomial f(x)

f(x) = x² - 3x + 2

To find

1/α + 1/β

Solution

let us first find the values of :

• Sum of the zeroes

=> α + β = -(coefficient of x) /coefficient of x²

=> α + β = -(-3)/1

=> α + β = 3

• Product of the zeroes

=> α × β = constant term/ coefficient of x²

=> α × β = 2/1

=> α × β = 2

Now

1/α + 1/β = (α + β)/α × β {Taking LCM}

=> 3/2 (Answer)