Answer:
- 3/2 ±sqrt(17)/2 = k
Explanation:
Area of a triangle is
A = 1/2 bh
1.5 = 1/2 b*h
b = distance between the x intercepts
h = y intercept
y=0.5(x−3)(x+k)
The x intercepts are 3, -k
Distance between them is (3--k) = 3+k so b = (3+k)
The y intercept is .5(-3 * k) = 1.5k so h = 1.5k
Substituting into the equation for A
1.5 = .5 (3+k) (1.5k)
1.5 = .75k(3+k)
Divide by .75 on each side
1.5/.75 = k(3+k)
2 = k(3+k)
2 = 3k+k^2
2 = k^2 +3k
We will need to complete the square
(3/2) ^2 =9/4 is what we need to add to each side
2+9/4 = k^2 +3k +9/4
8/4 + 9/4 = (k+3/2)^2
17/4 = (k+3/2)^2
Take the square root of each side
±sqrt(17/4) = sqrt( (k+3/2)^2)
±sqrt(17/4) = k+3/2
Subtract 3/2 from each side
- 3/2 ±sqrt(17/4) = k
We know the square root of (a/b) =sqrt(a)/sqrt(b)
- 3/2 ±sqrt(17)/sqrt(4) = k
- 3/2 ±sqrt(17)/2 = k