<p>A quadratic curve is given by $y=hx^2-2x-9h+6$, where $h$ is a constant.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show that the equation $y=0$ has real roots for all values of $h$ except $h=0$<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">State the value of $h$ in the case where $y=0$ has two real and equal roots.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Given that the line $y=2x-h-12$ meets the curve $y=hx^2-2x-9h+6$, find the range of values of $h$.<span class="inline-marks">[5]</span></div></li></ol>

A quadratic curve is given by $y=hx^2-2x-9h+6$, where $h$ is a constant.

Show that the equation $y=0$ has real roots for all values of $h$ except $h=0$

State the value of $h$ in the case where $y=0$ has two real and equal roots.

Given that the line $y=2x-h-12$ meets the curve $y=hx^2-2x-9h+6$, find the range of values of $h$.

Quadratic Equations and Inequalities - Nature of Roots of Quadratic Equations

Quadratic Equations and Inequalities - Nature of Roots of Quadratic Equations