Moderate -0.8 This is a straightforward multi-part question testing standard discriminant knowledge and tangency conditions. Part (i) is direct calculation, part (ii) is routine interpretation, and part (iii) requires setting equations equal and showing discriminant equals zero—all textbook procedures with no problem-solving insight needed. Easier than average C1 material.
7. (i) Calculate the discriminant of \(x ^ { 2 } - 6 x + 12\).
(ii) State the number of real roots of the equation \(x ^ { 2 } - 6 x + 12 = 0\) and hence, explain why \(x ^ { 2 } - 6 x + 12\) is always positive.
(iii) Show that the line \(y = 8 - 2 x\) is a tangent to the curve \(y = x ^ { 2 } - 6 x + 12\).
7. (i) Calculate the discriminant of $x ^ { 2 } - 6 x + 12$.\\
(ii) State the number of real roots of the equation $x ^ { 2 } - 6 x + 12 = 0$ and hence, explain why $x ^ { 2 } - 6 x + 12$ is always positive.\\
(iii) Show that the line $y = 8 - 2 x$ is a tangent to the curve $y = x ^ { 2 } - 6 x + 12$.\\
\hfill \mbox{\textit{OCR C1 Q7 [9]}}