Question

If one root of px 2+ qx + 2 = 0 is the inverse of each other, then prove that p = 2. ​

Answer 1

Let the roots of equation be $\alpha$ and $\beta$

Now the product of roots is given by

$\alpha \beta = \frac{c}{a}$

Putting $\beta = \frac{1}{\alpha}$ we get

$\alpha \times \frac{1}{\alpha} = \frac{c}{a} \\ 1 = \frac{c}{a} \\ c = a$

i.e. p=2