Determine the value(s) of k for which x2 + (k-2)x - 2k = 0 has equal and real roots.
Hello, xxlvh!
Determine the value(s) of $\displaystyle k$ for which .$\displaystyle x^2 + (k-2)x - 2k \:= \:0$
has equal and real roots.
We're expected to know that a quadratic has equal roots if its discriminant is zero.
. . That is: .$\displaystyle b^2-4ac \:=\:0$
We have: .$\displaystyle a \:= \:1,\;b \:= \:k-2,\;c \:= \:\text{-}2k$
Therefore: .$\displaystyle (k-2)^2 - 4(1)(\text{-}2k) \:=\:0$ . . . . now solve for $\displaystyle k.$