If α and β are the roots of $2x^2-11x+5=0$, the equation whose roots are −α and −β is:

Negating both roots reverses the sign of their sum but leaves their product unchanged, so only the middle coefficient flips: replacing $x$ by −$x$ turns $2x^2-11x+5$ into $2x^2+11x+5.(5x^2-11x+2=0$ is the equation for the reciprocals, not the negatives; the options with −5 as the constant change the sign of the product too, which negating both roots never does.) The roots 5 and 1/2 become −5 and −1/2, and $2x^2+11x+5=(x+5)(2x+1)$.