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Daniel J Smith Custom TMUA Set A Paper 1 · Q14

Paper 1Algebra

Let aa, bb, cc be real constants with a>0a>0 and c≠0c\neq0.

Suppose the inequality ax2+bx+c>0ax^2+bx+c>0 has solution set

x<rorx>sx<r\quad\text{or}\quad x>s

where r<sr<s

In terms of rr, ss and cc, what is the solution set of

a(cx)2+b(cx)+c>0 ?a(cx)^2+b(cx)+c>0\ ?
Ax<crx<cr or x>csx>cs
Bx<rcx<\frac rc or x>scx>\frac sc
Cx<csx<cs or x>crx>cr
Dx<scx<\frac sc or x>rcx>\frac rc
EIf c>0c>0: x<rcx<\frac rc or x>scx>\frac sc; if c<0c<0: x<scx<\frac sc or x>rcx>\frac rc
FIf c>0c>0: rc<x<sc\frac rc<x<\frac sc; if c<0c<0: sc<x<rc\frac sc<x<\frac rc
GIf c>0c>0: x<rcx<\frac rc or x>scx>\frac sc; if c<0c<0: x<rcx<\frac rc or x>scx>\frac sc

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