2. 2x^2 + 11x + k
We will have a double root when the discriminant = 0
So
11^2 - 4 * 2 * k = 0
121 - 8k = 0
121 = 8k
k = 121/8
1. x^2 - 7x + p
p = (7/2)^2 = 49/4
Factroization is ( x - 7/2)^2
Here : https://web2.0calc.com/questions/algebra_39593
sqrt ( 2085136k^4) = 1444k^2
sqrt ( 4100625) = 2025
Note that 2 (1444k^2) (2025) = 5848200k^2
(1444k^2 - 2025)^2 = 0
Take the sqrt
1444k^2 - 2025 = 0
1444k^2 = 2025 take both sqrts
38k = 45 38k = -45
k = 45 / 38 k = -45/38
BC has the slope [ -8 - 2 ] / [ 1 - - 3] = -10 / 4 = -5/2
The altitude through A will have the slope (2/5)
Writing an equation for a line containg this altitude, we have
y =(2/5) (x - 2) + 3
When x = 0, y = (2/5)(0 -2) + 3 = -4/5 + 3 = 11/5 = 2.2
Here : https://web2.0calc.com/questions/question8
Simplify
x^2 + 12x - 3 = 0
Sum of the roots = a + b = -12
(a - 4) + ( b - 4) = (a + b) - 8 = -12 - 8 = -20
The sum of the interior and exterior angles = 180
So....the interior angle = 120°
To find the number of sides, n
(n - 2) 180 / n = 120
(n -2) 180 = 120n
180 n - 360 = 120n
60n = 360
n =360 / 60 = 6
The side length = p / 6
A = (6) (1/2) (p/6)^2 sin (60°)
3/2 = 3 (p^2 / 36) sqrt (3) / 2
1 = sqrt (3) * p^2 / 36
36 / sqrt (3) = p^2
36/ 3^(1/2) = p^2 take the +sqrt of both sides
p = 6 / 3^(1/4)
Side length = [ 6/ 3^(1/4)] / 6 = 1/3^(1/4) ≈ .759
7*x + 1*8x = 7x + 8x = 15x
