Question

4s square-4s+1 with the split terms and formula of alfa and beta

Answer 1

Splitting the middle term:

4s² - 4s + 1 = 0

4s² - 2s - 2s + 1 = 0

(-2 * -2 = 1 * 4 and -2 + -2 = -4)

2s(2s - 1) - 1(2s - 1) = 0

(2s - 1)(2s - 1) = 0

(2s - 1)² = 0

s = 1/2.

Alpha, Beta stuff:

D = b² - 4ac

Here, a = 4, b = -4 and c = 1.

D = (-4)² - 4*4*1 = 16 - 16 = 0.

Now, α = (-b + √D)/2a, ß = (-b -√D)/2a

So, α = (-(-4) + 0)/2*4 = 4/8 = 1/2

And, ß = (-(-4) - 0)/2*4 = 4/8 = 1/2.