The curve $y = mx^2 - 12x + 2(x^2 + m - 1)$ lies entirely below the $x$-axis for all real values

Question

The curve $y = mx^2 - 12x + 2(x^2 + m - 1)$ lies entirely below the $x$-axis for all real values of $x$. Find the largest integer value of $m$.[5] Show that the roots of the equation $2x^2 - 3(1 - x) = -p$ are real if $p \le 4\frac{1}{8}$.[4]

Accepted Answer

(a) $m=-6$ (b) $p\le\frac{33}{8}=4\frac18$ (shown)

2024 CGSS P2 Q1

2024 CGSS P2 Q1

Video Solution:

Solution:

Solution locked