Question

Hallar la ecuación polinomica de f (x)=1/2.(x+4)^2-2

Answer 1

f(x) = (1/2)(X + 4)² - 2

Desarrollemos primero el el binomio cuadrado:

(X + 4)² = (X)² + 2(X)(4) + (4)² = X² + 8X + 16

Ahora el producto de (1/2)(X² + 8X + 16)

(1/2)(X² + 8X + 16) = X²/2 + 4X + 8

Finalmente la resta (1/2)(X + 4)² - 2

f(x) = X²/2 + 4X + 8 - 2

f(x) = X²/2 + 4X + 6

Hallamos las Raices

0 = X²/2 + 4X + 6

Donde a = 0.5; b = 4;  c = 6

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-(4)\pm \sqrt{(4)^2-4(0.5)(6)}}{2(0.5)}$

$X=\frac{-4\pm \sqrt{16-12}}{1}$

$X=\frac{-4\pm \sqrt{4}}{1}$

$X=\frac{-4\pm \ 2}{1}$

X1 = [-4 + 2]/1

X1 = -4 + 2 = -2

X2 = [-4 - 2]/1

X2 = -4 - 2 = -6

Raices: X1 = -2 , X2 = -6