The roots of the equation $x^2+3x-9=0$ are $\alpha$ and $\beta$. Without solving the equation,

Question

The roots of the equation $x^2+3x-9=0$ are $\alpha$ and $\beta$. Without solving the equation, find the value of each of the following. $(\alpha+2)(\beta+2)$ $\dfrac{1}{\alpha+2}+\dfrac{1}{\beta+2}$

Accepted Answer

(a) $-11$ (b) $-\frac{1}{11}$

Products of shifted roots

Products of shifted roots

Solution:

Solution locked