Quadratic Function

Paper for grade X SMA 1 Blitar ( X-8 and X-9 )
Day : Friday, September 24
Please submit your work next week ( Oct, 2 )

1. Find the range of values of x for which : 3(x-1)^2 + 24 > 2 ( x + 1)^2
2. Find the values of k for which the quadratic equation 9x^2 - kx + (k - 7) = 0 has
(i) one positive and one negative root
(ii)one root is twice the value of the other
3. Show that for all real values of p and q, y = - (1+p^2)x^2 + 2pqx - (2q^2+1) is
is always negative for all real values of x.
4. Show that x^2 - x + 1 is always positive for all real values of x. Hence, or
otherwise, find the range of values of a if the inequality
( x^2 + ax - 2):( x^2 - x + 1) < 2 is satisfied for all real values of x.