Evaluate the discriminant for x2-5x+4=0
1 answer:
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Answer:
(d) (4, -10)
Step-by-step explanation:
We are asked to identify the point that falls on a line defined by parametric equations.
<h3>Vector form equation</h3>The parametric equation can be written in a number of forms One of these is a vector form, in which some multiple of a vector is added to a known point.
(x(t), y(t)) = (1/2t +4, 2t -10) = (4, -10) +(1/2t, 2t)
(x, y) = (4, -10) +(t/2)(1, 4)
Clearly, when t=0, one point on the line will be (4, -10) — the last of the offered choices.
<h3>Other forms</h3>Another form of the equation can be had by solving the x(t) and y(t) equations for t, then equating those values.
x = 1/2t +4 ⇒ 2(x -4) = t
y = 2t -10 ⇒ (y +10)/2 = t
Equating these gives ...
2(x -4) = (y +10)/2 . . . . t = t
4x -16 = y +10 . . . . . . . multiply by 2
4x -y = 26 . . . . . . . . . add 16-y to put in standard form
Dividing by 26 gives intercept form:
x/6.5 +y/(-26) = 1 . . . . . x-intercept: 6.5, y-intercept: -26.
This tells you the value of y will be negative for all x-values less than 6.5. All of the offered points have x-values less than that, so the only viable answer choice is (4, -10).
