Make an algebraic estimate if the curve y = x^2 − (4x/5) + (1/5) has zero points.
estimate of what?
This question seems odd as hell, sorry. algebraisk bedömning in swedish but that comes out to algebraic estimate or algebraic assessment, and the rest is pretty much as is it, above a curve/zero points.
To find the zero points of the curve y = x^2 − (4x/5) + (1/5), we need to determine the values of x for which y is equal to zero.
To do this algebraically, we set y = 0 and solve for x. The equation becomes:
x^2 − (4x/5) + (1/5) = 0
To make the equation easier to work with, we can multiply the entire equation by 5 to eliminate the fractions:
5(x^2) - 4x + 1 = 0
Now, we can either factor the quadratic equation or use the quadratic formula to solve for x. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 5, b = -4, and c = 1. Substituting these values:
x = (-(-4) ± √((-4)^2 - 4(5)(1))) / (2(5))
x = (4 ± √(16 - 20)) / 10
x = (4 ± √(-4)) / 10
Since we have a negative square root, we can conclude that the quadratic equation has no real solutions. Therefore, the curve y = x^2 − (4x/5) + (1/5) has no zero points.