Question

1. Oblicz w(2) jeśli w(x) = x³ - 3x²+ 2x - 1

2. Oblicz w(-1) jeśli w(x) = 2x³ - x² + 5

3. Oblcz m jeśli w(x) = x³ - 2mx + 4 i w(1) = 4

4. Oblicz w + v, w - v, w * v jeśli

w(x)= x³ + 2x

v(x) = x³ - 1

Answer 1

1. Oblicz w(2) jeśli w(x) = x³ - 3x²+ 2x - 1

W(2) = 2³ - 3*2² +2*2 -1

W(2) = 8 - 12 +4 -1

W(2) = 12 -13

W(2) = -1

 

2. Oblicz w(-1) jeśli w(x) = 2x³ - x² + 5

W(-1) = 2*(-1)³ -(-1)² +5

W(-1) = 2*(-1) - 1 +5

W(-1) = -2 -1 +5

W(-1) = -3 +5

W(-1) = 2

 

3. Oblcz m jeśli w(x) = x³ - 2mx + 4 i w(1) = 4

 

W(x) = x³ -2mx +4

W(1) = 4

W(1) = 1³ -2*m*1 +4 = 4

          1 -2m +4 -4 = 0

            -2m +1 = 0

            -2m = -1       /:(-2)

              m = ½

 

4. Oblicz w + v, w - v, w * v jeśli

w(x)= x³ + 2x

v(x) = x³ - 1

 

w + v = x³ + 2x + x³ - 1

w +v = 2x³ +2x -1

 

w- v = x³ + 2x - ( x³ - 1)

w -v = x³ +2x -x³ +1

w -v = 2x +1

 

w*v = ( x³ + 2x)*(x³ - 1)

w*v = x⁶-x³ +2x⁴-2x

w*v = x⁶+2x⁴- x³ -2x