1. ## two quadratic equation problems

1. Prove
$a^2 + b^2+c^2-ab-ac-bc > 0$

2. Let $\alpha$ and $\beta$ be the roots of the equation $x^2 +kx +(p-k-1)=0$, where p and k are positive real numbers.
(i) Find the quadratic equation whose roots are $\alpha -1$and $\beta -1$
(ii) If p is prime and $\alpha$, $\beta$ are integers, show that k = p - 1

For question 2 I have trouble in (ii).

2. Originally Posted by cakeboby
2. Let $\alpha$ and $\beta$ be the roots of the equation $x^2 +kx +(p-k-1)=0$, where p and k are positive real numbers.
(i) Find the quadratic equation whose roots are $\alpha -1$and $\beta -1$
(ii) If p is prime and $\alpha$, $\beta$ are integers, show that k = p - 1

For question 2 I have trouble in (ii).

You should find in (i) $x^2 + (k+2)x + p = 0$
If p is prime then $\alpha-1=1$ and $\beta-1=p$ (or the other way)