CAIE P1 2020 Specimen — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionSpecimen
TopicQuadratic Functions

11 Th fo tin f is d fin f \(\mathbf { o } x \in \mathbb { R } , \quad x \mapsto x ^ { 2 } + a x + b , \mathrm { w } \mathbf { b }\) re \(a\) ad \(b\) are \(\mathrm { c } \mathbf { B }\) tan s .
  1. It is g it h t \(a = 6\) d \(b = 8\) Fid b rag 6 f .
  2. It is g ven in tead th \(\mathrm { t } a = 5\) ad th t th ro s \(\mathbf { 6 }\) the eq tin \(\mathrm { f } ( x ) = 0\) are \(k\) ad \(z k\), wh re \(k\) is a CB tan. Fid b le s \(6 b\) ad \(k\).
  3. Sha th tif the equ tif \(( x + a ) = a \mathbf { h }\) so eal ro sth \(\mathrm { n } a ^ { 2 } < ( 4 b - a )\).