Find the roots of the equation $b\left| x-a \right|=x-ab$, where $a$ and $b$ are constants. [2] If $

Question

Find the roots of the equation $b\left| x-a \right|=x-ab$, where $a$ and $b$ are constants. [2] If $a write down a condition for $b\left| x-a \right|=x-ab$ to have a negative real root. [1] using the same condition from (a), on the same axes, sketch the graphs of $y=x-ab$ and $y=b\left| x-a \right|$, [2] Hence solve the inequality $b\left| x-a \right|\ge x-ab$. [1] Deduce the set of values of $x$ for which $-b\left| {{\mathrm{e}}^{x}}+a \right|\le {{\mathrm{e}}^{x}}+ab$. [2]

Accepted Answer

(i) x = 0 or 2ab/(1+b); (ii)(a) b < -1; (ii)(b) x ≤ ln(-2ab/(1+b))

2020 ACJC P1 Q4

2020 ACJC P1 Q4

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