Miejscami zerowymi funkcji
f(x)=ax2 + bx + 2 są liczby (-2) i 9. Wyznaczy parametry a i b
Dam naj. Pozdrawiam
f(-2)=0
f(9)=0
więc
a*(-2)²+b*(-2)+2=0
a*9²+b*9+2=0
4a-2b=-2 /:2
81a+9b=-2
2a - b = -1 /*9
81a + 9b = -2
18a - 9b = -9
99a = -11 /:99
a = -11/99
a = - 1/9
2a - b =-1
b = 2a - 1
b = 2*(-1/9) - 1
b = -2/9 - 1
b =-1 2/9
więc:
f(x)=-1/9x² - 1 2/9x + 2
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f(-2)=0
f(9)=0
więc
a*(-2)²+b*(-2)+2=0
a*9²+b*9+2=0
4a-2b=-2 /:2
81a+9b=-2
2a - b = -1 /*9
81a + 9b = -2
18a - 9b = -9
81a + 9b = -2
99a = -11 /:99
a = -11/99
a = - 1/9
2a - b =-1
b = 2a - 1
b = 2*(-1/9) - 1
b = -2/9 - 1
b =-1 2/9
więc:
f(x)=-1/9x² - 1 2/9x + 2