Let the inequalities $y( - 1) - 4,y(1) 5$ are known to hold for $y = {ax

Question

Let the inequalities $y( - 1) > - 4,y(1) < 0$ and $y(3) > 5$ are known to hold for $y = {ax}^{2} + bx + c$, then

Accepted Answer

$a - b + c > - 4$$$\begin{matrix} a + b + c < 0 & \Rightarrow & - a - b - c > 0 & \ & \Rightarrow & & - 2b > - 4 \ & \Rightarrow & & 9a + 3b + c > 5 \ & & & - a - b - c > 0 \ & \Rightarrow & & 8a + 2b > 5 \ & & & 8a + 4 > 8a + 2b > 5 \end{matrix} \Rightarrow \ b < 2$$

Question

Options

Solution

More Quadratic Equation Questions