Question

If alpha and beta are the zeroes of the polynomial 5x^2-7x+2 then find the sum of their reciprocals

Answer 1

Here alpha + beta = -b/a
aloha×beta = c/a
Here a,b and c are 5, -7 and 2

Now if we take reciprocal
1/alpha + 1/beta = alpha + beta divided by alpha×beta.

Substitute values to get your answer.


Hope you get your answer.

Answer 2

Solving the polynomial by factorisation
$5 {x}^{2} - 5x - 2x + 2 = 0 \\ 5x(x - 1) - 2(x - 1) = 0 \\ (5x - 2)(x - 1) = 0 \\ x = 1 \: or \: \frac{2}{5}$
So the reciprocals of the zeros are 1 and 5/2