Question

wyznacz pierwiastki wielomianow

Oblicz wartość wyrażenia.

log4 + log3 // log36-log3 - log₂8

Answer 1

a)

W(x) = x³ + 4x² - 2x - 8 = x²(x + 4) - 2(x + 4) = (x  +4)(x² - 2) = (x + 4)(x - √2)(x + √2)

pierwiastki wielomianu to: -4 ; -√2 ; √2

 

b)

W(x) = x² + x - 2

           Δ = 1 - 4 * 1 * (-2) = 1 + 8 = 9

          √Δ = 9

          x1 = (-1 - 9)/2 = -10/2  = -5

          x2 = (-1 + 9)/2 = 8/2 = 4

pierwiastki wielomianu to: -5 ; 4

 

 log4 + log3 // log36-log3   - log₂8 = log (4 * 3) / log (36 : 3)  - log2 2³ =

log 12 / log 12 - 3log2 2 = 1 - 3 * 1 = 1 - 3 = -2