The given set of equations are:
15x−y=82
6x−5y=−4
9x+4y=17
Now on solving the above equation by taking two at a time and plotting the diagram we get,

(α,β)≡(31+5+6,32−7+8)≡(4,1)
Hence, α+2β=6 and 2α−β=7
The required equation is (x−6)(x−7)=0
Equation x2−13x+42=0
Hence this is the required option.