How to solve a polynomial homogeneous matrix I am having trouble solving the solutions for this problem. It states:
The polynomials, $f_1(x)=x-2$, $f_2(x)=x^2-5x+4$, $f_3(x)=3x^2-4x$, $f_4(x)=x^2-1$ are linearly dependent since $f_1(x) + f_2(x) - f_3(x) + 2f_4(x) = 0$.
But how did they get coefficents? 
My attempt:
$x^2(b+3c+d) +x(a-5b-4c)+(-2a+4b-1d) = 0$ but when I solve it, it doesn't give me the correct coefficents of the polynomial.

You solve $b+3c+d=0, a-5b-4c=0, -2a+4b-d=0$. There are 3 equations in 4 unknowns so there are infinitely many solutions,  $c$ is a free variable and $a=b=-c, d=-2c$ If you let $c=-1$ then you get the solution $a=1, b=1, d=2$ as desired.
