Given that p2 + q2 = 13 and that pq = 6, construct the quadratic equation whose roots are p^2 and and q^2. Find all the possible values of p.
I have already constructed the equation. it's something like x2 - 13x + 36.
but i could only get positive 2 and 3 for the value of p. but my answer states that there should be both positive and negative 2 and 3. how do i get the negative?
you should get x = 9 or 4
then p^2 = 9 or 4 (note that when p^2 = 9, q^2 = 4 and vice versa)
hence p = 3, -3 or 2, -2 (because de square of a negative number gives u positive as well)