Question

If alpha and beta are zeros of x2-3x+5 then find1/alpha+1/beta

Answer 1

$\large\rm { f(x) = x^{2}-3x+5}$

$\large\rm { a = 1}$

$\large\rm { b = -3}$

$\large\rm { c = 5}$

$\large\rm { \because \alpha \ \sf{and} \ \beta}$ are the zeros of the polynomial.

$\large\rm { \therefore}$ sum of roots : $\large\rm { \frac{-b}{a}}$

$\large\rm { \alpha + \beta = \frac{-(-3)}{1} }$

$\large\rm { \alpha + \beta = 3}$

product of roots :

$\large\rm { \frac{c}{a}}$

$\large\rm { \alpha \beta = 5/1 = 5}$

$\large\rm { \therefore \frac{1}{ \alpha} + \frac{1}{ \beta} = \frac{ \alpha + \beta}{ \alpha \beta} }$

From eq. 1&2 we have:

→ 3/5

Hence, 3/5 is the required answer.