Science:Math Exam Resources/Courses/MATH307/December 2012/Question 01 (d)/Statement

In this question we will work with polynomials of degree 3 written

$\displaystyle p(x)=a_{1}x^{3}+a_{2}x^{2}+a_{3}x+a_{4}$

(d) Using the equation in (c) find the equation Cs=c satisfied by $\mathbf {s} =[s_{1},s_{2}]^{T}$ if p(x)

(i) has coefficient vector $\mathbf {a} =s_{1}\mathbf {a} _{1}+s_{2}\mathbf {a} _{2}$ (and therefore has zero slope at x = 0 and x = 2).

(ii) passes through the points (0,1), (1,2) and (2,2).

Does this equation have a solution? Give a reason.