It is given that $y=\frac{2{{x}^{2}}+3}{x-2},x\in \mathbb{R},x\ne 2$. Sketch the graph of \(y

Question

It is given that $y=\frac{2{{x}^{2}}+3}{x-2},x\in \mathbb{R},x\ne 2$. Sketch the graph of $y=\frac{2{{x}^{2}}+3}{x-2}$ and label clearly the equations of the asymptotes and intercepts if any. The graph of $y=\frac{2{{x}^{2}}+3}{x-2}$ cannot lie between values $p$ and $m$, where $p>m$ . State the value of $p$ and $m$ . By means of a graphical argument, state the maximum number of real roots the equation $kx\left( x-2 \right)-2{{x}^{2}}=3$ have.

Accepted Answer

(ii) $p=8+2\sqrt{22}$, $m=8-2\sqrt{22}$ (iii) Maximum number of real roots is $2$

ACJC Tutorial 2 Q8

ACJC Tutorial 2 Q8

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