Question

x2-2x+k
has equal roots

them find the value of K​

Answer 1

Step-by-step explanation:

x2-2x+k=0

Sinchit has equal roots

so, b2-4ac=0

(-2)(-2) - 4×1×k=0

4-4k=0

-4k=-4

k=1

So 1 is equal to k

Answer 2

Answer:

Equal roots means that x² - 2x + k is a perfect square.

Now we know that a perfect square can be represented in the form of:

(a + b)² = a² + 2ab + b²

So:

x²   - 2x    + k

↓       ↓       ↓

a² + 2ab + b²

x² = a²

$\sqrt{x^2} = \sqrt{a^2}$

x = a

a = x

Similarly,

2ab = -2x

ab = -x

(and since a = x)

xb = -x

b = -1

Thus

b² = $(-1)^2$

$b^2 = 1\\k = 1$