Final answer:
The value of k in the quadratic equation 5x²-x-k=0, with the difference between its roots being 1.8, is 0.76.
Step-by-step explanation:
The question involves finding the value of k in the quadratic equation 5x²-x-k=0 given that the difference between its roots is 1.8. We know that the difference between the roots of a quadratic equation ax²+bx+c=0 can be found using the relationship difference = √(b²-4ac)/|a|.
For the quadratic equation 5x²-x-k=0, we have:
- a = 5, b = -1, and c = -k.
Therefore, we can set up the equation according to the difference of roots:
- 1.8 = √((-1)²-4(5)(-k))/|5| = √(1 + 20k)/5
Squaring both sides and solving for k gives us:
- (1.8)² = (1+20k)/5
- 3.24 * 5 = 1 + 20k
- 16.2 = 1 + 20k
- k = (16.2 - 1)/20 = 0.76
Hence, the value of k is 0.76.