1.33: Completing the Square and Unequal Roots

4PM1/1/January/2019 — Question 5 · 10 marks

f(x)=2x2+7x−4.f(x)=2x^2+7x-4.
Given that f(x)\displaystyle f(x) can be written in the form
A(x+B)2+C,A(x+B)^2+C,
(a) find the value of A\displaystyle A, the value of B\displaystyle B and the value of C\displaystyle C.
(3)
(b) Write down
(i) the minimum value of f(x)\displaystyle f(x),
(ii) the value of x\displaystyle x at which this minimum occurs.
(2)
The equation
f(x)=px−6f(x)=px-6
has unequal real roots.
(c) Find the set of possible values of p\displaystyle p.
(5)