If one of the roots of the quadratic question x2−x=k𝑥2-𝑥=𝑘 be square of the other, then k=

Let's denote the roots of the quadratic equation as a and b. According to the problem, one root is the square of the other, so we can say a = b^2.

The sum of the roots of a quadratic equation is given by -B/A, where B is the coefficient of x and A is the coefficient of x^2. In this case, A = 1 and B = -1. So, a + b = -(-1)/1 = 1.

The product of the roots of a quadratic equation is given by C/A, where C is the constant term. In this case, C = -k and A = 1. So, ab = -(-k)/1 = k.

Substituting a = b^2 into these equations, we get:

b^2 + b = 1 and b^3 = k.

Solving the first equation for b, we get b = -1 ± sqrt(1 + 4b^2) / 2. Since b must be real, we discard the negative root, leaving b = (-1 + sqrt(5)) / 2.

Substituting this value into the second equation, we get k = ((-1 + sqrt(5)) / 2)^3 = -1.