Question

If the equation $x^2-2kx-2x+k^2=0$ has equal roots the value of k must be

• A. zero
• B. either zero or $-\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. either $\frac{1}{2}$ or $-\frac{1}{2}$

Answer 1

Answer: (C)

$-\frac{1}{2}$

The equation $x^2-2(k+1)x+k^2=0$ will have equal roots when $D=0$,

$D=b^2-4ac,$

$⟹2(k+1{)}^2-4(1\left)\right(k{)}^2=(k+1{)}^2-k^2$

$\therefore ⟹2k+1=0k=-1/2$