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Gunshp
@Gunshp
April 2020
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Determine o polinômio do 2° grau tal que p (0)=3, p (1)=7 e p (-2)=9.
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Verified answer
P(x) = ax2 + bx + c
p(0) = 0+0 + c = 3==> c = 3
p(1) = a(1)2 + (1)b + c= 7 ==> a + b + c = 7
p(-2) = a(-2)2 + (-2)b + c= 9 ==> 4a -2b + c = 9
a + b + 3 = 7 ==> a + b = 7 -3 ==> a + b = 4(2)
4a -2b +3 = 9 ==> 4a - 2a = 9 -3 ==> 4a - 2b = 6(1)
2a + 2b = 8
4a - 2b = 6
6a = 14
a= 14
6
a + b = 4 ==> 14/6 + b = 4 ==> 14 + 6b = 24 ==> 6b = 24-14 ==> 6b=10
b = 10/6
c= 3
p(x) = ax2 + bx + c
p(x) = 14x2 + 10x + 3
6 6
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Verified answer
P(x) = ax2 + bx + cp(0) = 0+0 + c = 3==> c = 3
p(1) = a(1)2 + (1)b + c= 7 ==> a + b + c = 7
p(-2) = a(-2)2 + (-2)b + c= 9 ==> 4a -2b + c = 9
a + b + 3 = 7 ==> a + b = 7 -3 ==> a + b = 4(2)
4a -2b +3 = 9 ==> 4a - 2a = 9 -3 ==> 4a - 2b = 6(1)
2a + 2b = 8
4a - 2b = 6
6a = 14
a= 14
6
a + b = 4 ==> 14/6 + b = 4 ==> 14 + 6b = 24 ==> 6b = 24-14 ==> 6b=10
b = 10/6
c= 3
p(x) = ax2 + bx + c
p(x) = 14x2 + 10x + 3
6 6