a) W(x) = - 3 x³ + a x² + b x + 2 Mamy W(-1) = 4 czyli -3*(-1)³ + a*(-1)² - b + 2 = 4 3 + a - b +2 = 4 a - b = - 1 --------------- Mamy W(2) = 20 czyli -3*(2)³ + a *2² + 2 b + 2 = 20 - 24 + 4 a + 2 b + 2 = 20 4a + 2 b = 42 ---------------- Trzeba rozwiązać układ równań a - b = -1 ----> b = a + 1 4a + 2b = 42 --------------------------- 4a + 2*(a +1) = 42 4a + 2a + 2 = 42 6a = 40 a = 40 : 6 = 20/3 b = a +1 = 20/3 + 1 = 20/3 + 3/3 = 23/3 Odp. a = 20/3 oraz b = 23/3 ============================= b) W(x) =x⁴ + a x³ + b x² + 2 W(-3) = 11 zatem (-3)⁴ +a*(-3)³ + b*(-3)² + 2 = 11 81 - 27 a + 9 b + 2 = 11 -27 a + 9 b = - 72 W(1) = 7 zatem 1⁴ + a + b + 2 = 7 --------------------------------- a + b = 4 ----> b = 4 - a -27 a + 9 b = - 72 ------------------------------ - 27 a + 9*(4 - a ) = - 72 - 27 a + 36 - 9 a= - 72 - 36 a = - 108 a = - 108 : (36) = 3 b = 4 - a = 4 - 3 = 1 -------------------------------------- Odp. a = 3 oraz b = 1 ========================================
a) W(x) = -3x³+a²+bx+2 W(-1)=4 W(-1)= -3*(-1)³+a*(-1)²+b*(-1)+2 W(-1) = 3+a-b+2 W(-1)=5+a-b 4=5+a-b a-b=-1 b=a+1 W(2)=-3*2³+a*2²+b*2+2 W(2)=-24+4a+2b+2 W(2)=-22+4a+2b 20=-22+4a+2b 42=4a+2b 42=4a+2(a+1) 42=4a+2a+2 40=6a a=6⅔ b=a+1=6⅔+1=7⅔ b) W(x)=x⁴+ax³+bx²+2 W(-3)=11 W(-3)=(-3)⁴+a*(-3)³+b*(-3)²+2 W(-3)=81-27a+9b+2 W(-3)=83-27a+9b 11=83-27a+9b -72=-27a+9b/:9 -8=-3a+b b=-8+3a W(1)=1⁴+a*1³+b*1²+2 W(1)=1+a+b+2 W(1)=3+a+b 7=3+a+b 4=a+b 4=a+-8+3a 12=4a/:4 a=3 b=-8+9=1
