Show that $3x^2 - 5x + 21$ is always positive for all real values of $x$.[3] The curve \(y

Question

Show that $3x^2 - 5x + 21$ is always positive for all real values of $x$.[3] The curve $y = ax^n$, where $a$ and $n$ are constants, passes through $(2, 48)$, $(3, 108)$ and $(k, 192)$. Find the values of $a$, $n$ and $k$ where $k > 0$.[3]

Accepted Answer

(i) $3x^2-5x+21>0$ for all $x\in\mathbb R$ (shown) (ii) $a=12$, $n=2$, $k=4$

2024 CCHY P1 Q3

2024 CCHY P1 Q3

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