Find the exact roots of the equation $\left| 3{{x}^{2}}+8x-3 \right|=3-x$. [3] On the same axes, ske

Question

Find the exact roots of the equation $\left| 3{{x}^{2}}+8x-3 \right|=3-x$. [3] On the same axes, sketch the curves with equations $y=\left| 3{{x}^{2}}+8x-3 \right|$ and $y=3-x$. Hence solve exactly the inequality $\left| 3{{x}^{2}}+8x-3 \right|\ge 3-x$. [4]

Accepted Answer

$x=\dfrac{-3\pm \sqrt{17}}{2},\; 0,\; -\dfrac{7}{3}$

2023 YIJC P1 Q3

2023 YIJC P1 Q3

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