Alpha , beta are zeroes of x square -3x -1 then find 1/ alpha + 1/ beta
To find 1/alpha + 1/beta, we need to first find the values of alpha and beta.
Given that alpha and beta are the zeroes of x^2 - 3x - 1 = 0, we can use the formula for finding the zeroes of a quadratic equation:
alpha, beta = (-b ± √(b^2 - 4ac))/(2a)
Here, the coefficients are:
a = 1
b = -3
c = -1
Substituting the values into the formula, we get:
alpha, beta = (-(-3) ± √((-3)^2 - 4(1)(-1)))/(2(1))
= (3 ± √(9 + 4))/2
= (3 ± √13)/2
So, alpha = (3 + √13)/2 and beta = (3 - √13)/2.
Now, let's find 1/alpha + 1/beta:
1/alpha + 1/beta = [(1*beta + 1*alpha)/(alpha*beta)]
= (alpha + beta)/(alpha*beta)
Using the sum and product of the roots formula for a quadratic equation:
alpha + beta = -(-3) = 3
alpha * beta = -1/1 = -1
Thus, 1/alpha + 1/beta = (alpha + beta)/(alpha * beta)
= 3/-1
= -3
Therefore, 1/ alpha + 1/ beta = -3.