One root of x²−(k+2)x+2k=0 is twice the other root. Which set gives all possible positive values of k?

Question

G1 Physics · Accepted Answer

Let the roots be r and 2r. Their sum gives 3r=k+2, while their product gives 2r²=2k, so k=r². Hence 3r=r²+2 ⇒ r²−3r+2=0 ⇒ r=1 or 2. Therefore k=r² gives k=1 or 4.