Question

The attachment shows the graph of frac{7x^2 - 6}{x+5}. Use the graph to find the range of values of k for which \[frac{7x^2 - 6}{x+5} = kx + frac{1}{2}\] has two distinct real roots. Note that the domain of x is [-1 , 1.5]

Answer 1

Errata:

Equation of curve:
\[y = \frac{7x^2 - 6}{x+5}\]

Equation of question (find the range...)
\[\frac{7x^2 - 6}{x+5} = kx + \frac{1}{2}\]

Answer 2

The graph