Question

rozloz wielomian w na czynniki a)w(x) =5x do potegi 5 - 20x do potegi 3 b) w(x) = 2x do potegi 5 + 8x do potegi 4 - 10x do potegi 3

Answer 1

a) w(x)=5x⁵-20x³=5x³(x²-4)=5x³(x-2)(x+2)

b) w(x)=2x⁵+8x⁴-10x³=2x³(x²+4x-5)=2x³(x+5)(x-1)

Δ=b²-4ac

Δ=16-4*(-5)

Δ=16+20

Δ=36

√Δ=6

x1=(-4-6)/2=-10/2=-5

x2=(-4+6)/2=2/2=1

 

Answer 2

a) 5x5-20x3=5x3 (x2-4)= 5x3(x-2)(x+2)
b) 2x5+8x4-10x3=2x3(x2+4x-5)=2x3(x+5)(x-1)
x2+4x+5=0
a=1

b=4

c=-5

delta=b2-4ac=4*4-4*1*(-5)=16+20=36

pierwiastek z delty = 6

x1=-b-pierw. z delty / 2a = -4-6/2*1=-10/2=-5

x2=-b +pierw.z delty/2a=-4+6/2*1=2/2=1