Determine the value(s) of 'K' that will give (k-1)x^2-5x + 10= 0 two imaginary roots.
k so the thing I know is that the discriminant is d<0
so do I solve for k?
I know I would use this formula:
b^2-4ac but how would I get into a formula I can work with would I times the x^2 by -1 and k ? I am unsure could you point me in the right direction???? thanks! so much!
Yes, the discriminant b^2 - 4 ac must be <0 for two complex roots. In your case
a = k-1, b = -5 and c = 10, so the requiremens becomes
b^2 - 4 ac = 25 - 40 (k-1) < 0
k-1 < 5/8
k < 1 5/8
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:
(−5)^2 − 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.