If the roots of the quadratic equation $x^2-8x+k=0$ are equal, then the value of $k$ is

Solution

1. For a quadratic equation $a{x}^2+bx+c=0$ to have equal roots, the discriminant $D=b^2-4ac$ must be zero.
2. Substitute $a=1$, $b=-8$, and $c=k$ into the discriminant formula: $(-8{)}^2-4(1)(k)=0$.
3. Simplify the equation to $64 - 4k = 0$.
4. Solve for $k$ to get $k=16$.
5. Hence the answer is (B).