Rozłóż wielomian na czynniki i wyznacz jego pierwiastki
w(x)=x^4+8x^3+16x^2
w(x)=4x^4+20x^3+25x^2
w(x)=x^3+2x^2-3x
w(x)=x^3+3x^2+4x
w(x)=4x^4-5x^3+6x^2
w(x)=x^4-2x^3+6x^2
w(x)=x^4+8x^3+16x^2
w(x)=4x^4+20x^3+25x^2
w(x)=x^3+2x^2-3x
w(x)=x^3+3x^2+4x
w(x)=4x^4-5x^3+6x^2
w(x)=x^4-2x^3+6x^2
Odpowiedź:
1. w(x)=x^4+8x^3+16x^2
x^4 + 8 x^3 + 16 x^2 = 0
x^2 (x + 4)^2 = 0
x^2 = 0 lub (x + 4)^2 = 0
x = 0 lub (x + 4)^2 = 0
x = 0 lub x + 4 = 0
x = 0 lub x = -4
2. w(x)=4x^4+20x^3+25x^2
4 x^4 + 20 x^3 + 25 x^2 = 0
x^2 (2 x + 5)^2 = 0
x^2 = 0 lub (2 x + 5)^2 = 0
x = 0 lub (2 x + 5)^2 = 0
x = 0 lub 2 x + 5 = 0
x = 0 lub 2 x = -5
x = 0 lub x = -5/2
3. w(x)=x^3+2x^2-3x
x^3 + 2 x^2 - 3 x = 0
x (x - 1) (x + 3) = 0
x - 1 = 0 lub x = 0 lub x + 3 = 0
x = 1 lub x = 0 lub x + 3 = 0
x = 1 lub x = 0 lub x = -3
4. w(x)=x^3+3x^2+4x
x^3 + 3 x^2 + 4 x = 0
x (x^2 + 3 x + 4) = 0
x = 0 lub x^2 + 3 x + 4 = 0
x = 0 lub x^2 + 3 x = -4
x = 0 lub x^2 + 3 x + 9/4 = -7/4
x = 0 lub (x + 3/2)^2 = -7/4
x = 0
5.
w(x)=4x^4-5x^3+6x^2
4 x^4 - 5 x^3 + 6 x^2 = 0
x^2 (4 x^2 - 5 x + 6) = 0
x^2 = 0 lub 4 x^2 - 5 x + 6 = 0
x = 0 lub 4 x^2 - 5 x + 6 = 0
x = 0 lub x^2 - (5 x)/4 + 3/2 = 0
x = 0 lub x^2 - (5 x)/4 = -3/2
x = 0 lub x^2 - (5 x)/4 + 25/64 = -71/64
x = 0 lub (x - 5/8)^2 = -71/64
x = 0
6. w(x)=x^4-2x^3+6x^2
x^4 - 2 x^3 + 6 x^2 = 0
x^2 (x^2 - 2 x + 6) = 0
x^2 = 0 lub x^2 - 2 x + 6 = 0
x = 0 lub x^2 - 2 x + 6 = 0
x = 0 lub x^2 - 2 x = -6
x = 0 lub x^2 - 2 x + 1 = -5
x = 0 lub (x - 1)^2 = -5
x = 0