1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use QuadraticIdentities Stage 6 - Year 11 Mathematic (Preliminary)

2 Quadratic Identities If two quadratic expression are equivalent then the respective coefficients must be equal. ≡ If a 1 x 2 +b 1 x + c 1 ≡ a 2 x 2 + b 2 x + c 2 then a 1 = a 2 b 1 = b 2 c 1 = c 2

3 Quadratic Identities Find the values of m, p and q for which 2x 2 – x – 1 ≡ m(x + 1) 2 + p(x + 1) + q 2x 2 – x – 1 ≡ m(x 2 + 2x + 1) + px + p + q 2x 2 – x – 1 ≡ mx 2 + 2mx + m + px + p + q 2x 2 – x – 1 ≡ mx 2 + (2m + p)x + (m + p + q) m = 2 2m + p = – 1 2 x 2 + p = – p = – 1 p = – 5 m + p + q = – (-5) + q = – q = – 1 q = 2