(i) Express \(2x^2-10x+8\) in the form \(a(x+b)^2+c\), where a, b and c are constant and use your answer to state the minimum value of \(2x^2-10x+8\). [3]
(ii) Find the set of values of k for which the equation \(2x^2-10x+8=kx\) has no real roots. [4]
Question 02
The function f is defined by \(f(x)=x^2-4x+8\) for \(x \in R\).
(i) Express \(x^2-4+8\) in the form \((x-a)^2+b\). [2]
(ii) Hence find the set of values of x for which \(f(x) < 9\), giving your answer in exact form. [3]
Question 03
(a) Express \(16x^2-24x+10\) in the form \((4x+a)^2+b\). [2]
(b) It is given that the equation \(16x^2-24x+10=k\), where k is a constant, has exactly one root. Find the value of this root. [2]
Question 04
The equation of a curve is \(y=(2k-3) x^2-kx-(k-2)\), where k is a constant. The line \(y=3x-4\) is a tangent to the curve. Find the value of k. [5]
Question 05
Showing all necessary working, solve the equation \(4x-11x^{\frac 12}+6=0\). [3]
Question 06
By using suitable substitution, solve the equation \((2x-3)^2- \dfrac {4}{(2x-3)^2} -3=0\). [4]
Question 07
The equation of a line is \(y=mx+c\), where m and c are constant, and the equation of a curve \(xy=16\).
(a) Given that the line is a tangent to the curve, express m in terms of c. [3]
(b) Given instead that \(m=-4\), find the values of c for which the line intersects the curve at two distinct points. [3]
Question 08
(a) Find the values of the constant m for which the line y=mx is a tangent to the curve \(y=2x^2-4x+8\). [3]
(b) The function f is defined for \(x \in R\) by \(f(x)=x^2+ax+b\), where a and b are constants. The solutions of the equation \(f(x)=0\) are \(x=1\) and \(x=9\). Find:
(i) The values of a and b. [2]
(ii) The coordinates of the vertex of the curve \(y=f(x)\). [2]