Given that the curve $y = ax^2 + 2bx - 1$ lies entirely below the $x$-axis, determine the condit

Question

Given that the curve $y = ax^2 + 2bx - 1$ lies entirely below the $x$-axis, determine the conditions that must be applied to the constants $a$ and $b$. If $a$ and $b$ are both integers, state an example of the values of $a$ and $b$ which satisfy the conditions found in (i).

Accepted Answer

(i) $a<-b^2$ for a quadratic; also $(a,b)=(0,0)$ if the constant case is allowed. (ii) For example, $a=-5,b=2$.

2025 CHS PRELIMS P2 Q2

2025 CHS PRELIMS P2 Q2

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