Question

if the quadratic equation x^2-2x+k=0 has equal roots then find the value of k​

Answer 1

Answer:

${x}^{2} - 2x + k = 0$

$d = {b}^{2} - 4ac$

${2}^{2} - 4 \times 1 \times k$

$4 - 4k = d$

$if \: it \: ha \: two \: equa \: roots$

$d = 0$

$4 - 4k = 0$

$- 4k = - 4$

$k = \frac{ - 4}{ - 4}$

K =1

Hope it helps

Answer 2

$\huge{\underline{\underline{\sf{Answer: }}}}$

Given Equation,

$\sf{ x{}^{2} - 2x + k = 0 }$

On comparing with,

$\sf{ax {}^{2} + bx + c = 0 }$

Here,

a = 1, b = -2 and c = k

ATQ,

The roots of the equation are equal. Implies, discriminant of the equation is zero

$\rightarrow \: \sf{d = 0} \\ \\ \rightarrow \: \sf{b {}^{2} = 4ac } \\ \\ \rightarrow \: \sf{( - 2) {}^{2} = 4(1)(k)} \\ \\ \rightarrow \: \sf{4k = 4} \\ \\ \rightarrow \: \huge{ \sf{k = 1}}$

• For K = 1,given equation has equal roots