Question

If alpha and beta are the serious of the quadratic polynomials f(x) = kx^2+4x+4 such that alpha^2+beta^2=24 find the alpha^2-beta^2

Answer 1

Answer:

solved

Step-by-step explanation:

kx^2+4x+4 = 0

kx²+4x+4 = 0

x²+4x/k+4/k = 0

∝+β = - 4/k

∝β = 4/k

∝² + β² = (∝+β)² -2∝β = 16/k² - 8/k =24

16-8k = 24k²

2-k  = 3k²

3k²+k-2 = 0

3k²+k/3-2/3 = 0

k = (1±5)/6 = 1 , - 2/3

N = ∝²- β² = (∝+β)(∝-β) = -4/k(∝-b) =  (-4/k )√{ (∝+b)² -4∝β}

N = (-4/k )√{ 16/k² - 16/k} = (-16/k²) √ (1+k)

1st case    :  N = -16√2

2nd. case :  N = -16/√3 ÷ 4/3 = - 4/3√3 = - 4√3/9