## To determine the values of 'k' that will give two imaginary roots, you need to find the range of 'k' that satisfies the condition that the discriminant is less than zero.

The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, the equation is (k-1)x^2 - 5x + 10 = 0, so a = k-1, b = -5, and c = 10.

Substituting these values into the discriminant formula, you have:

(âˆ’5)^2 âˆ’ 4(k-1)(10) < 0

25 - 40(k-1) < 0

25 - 40k + 40 < 0

65 - 40k < 0

-40k < -65

k > 65/40

k > 13/8

Therefore, the range of 'k' that will give two imaginary roots is k > 13/8.