Mathematical Science Linear Integral Equations

For c ∈ ℝ, consider the following Fredholm integral equation \(\rm y(x)=1+x+cx^2+2\int_0^1(1-3xt)y(t)dt\) Then the values of c for which the integral equation admits a solution are  

1
-8
2
-6
3
2
4
6

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