Question

If equation x^2-2kx-2x+k^2 has two equal roots, then value of k?

Answer 1

To Remember :

• Sum of zeros = - Coefficient of x/Coefficient of x²

• Product of zeros = Constant Term/Coefficient of x²

Solution :

• Take - x as common where - will get cancel out due to - sign infront of (2k - 2).

$\bold{\Longrightarrow{{x}^{2} - 2kx - 2x + {k}^{2}}} \\ \bold{\Longrightarrow{{x}^{2} - x(2k + 2) + {k}^{2}}} \\ \\ \bold{\Longrightarrow{\alpha + \beta = 2k + 2}} \\ \bold{\Longrightarrow{\alpha = \beta}} \\ \bold{\Longrightarrow{2 \alpha = 2(k + 1)}} \\ \bold{\Longrightarrow{\alpha = \beta = k + 1}} \\ \\ \bold{\Longrightarrow{\alpha \beta = {k}^{2}}} \\ \bold{\Longrightarrow{(k + 1)(k + 1) = {k}^{2}}} \\ \bold{\Longrightarrow{{k}^{2} + k + k + 1 = {k}^{2}}} \\ \bold{\Longrightarrow{2k = 1}} \\ \bold{\Longrightarrow{k = \frac{1}{2}}}$

Answer : k = 1/2