two quadratic equation problems

**cakeboby** · Jul 12th 2010, 09:39 AM

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).

Thanks in advance.

**running-gag** · Jul 12th 2010, 11:05 AM

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).

Thanks in advance.

Hi

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)

I let you finish

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