Question

If alpha and beta are zeros of x^2 + 5x + 5 find a^-1 + b^-1

Answer 1

Hello,
The polynomial is
P(x) = x²+5x+5

Also, alpha and beta are the zeroes of the polynomial.
For quadratic polynomials the relation between the zeroes and the coefficients is
$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a}$

For p(x)
Sum of zeroes = (-5)
Product of zeroes = 5


We need to find the value of
$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } = \frac{ - 5}{5} = ( - 1)$

Hope this will be helping you....