Question

determine a e b reais em p(x)=ax3-2x2+bx-1 sabendo que 1 é raiz de p(x) e que p(2)=3

Answer 1

p(x)=ax3 -2x2 +bx-1 ===> p(1)=0
p(1)=a.1³ -2.1² +b.1 -1
p(1)= a -2 +b -1 =0
a+b = 3
b = 3 -a

p(x)=ax3 -2x2 +bx-1 ==> p(2)=3
p(2)=a.2³ -2.2² +b.2 -1= 3
8a -8 +2b -1 = 3
8a +2b = 12
8a +2(3-a) =12
8a +6 -2a = 12
6a = 6
a= 1 ✓

b = 3-a = 3-1 = 2 ✓

Answer 2

p(x)=ax*3-2x*2+bx-1

p(2)=3

p(2)=a.(2)*3-2(2)*2+2.(b)-1

p(2)=8a-2.(4)+2b-1

p(2)=8a-8+2b-1

p(2)=8a+2b-9

8a+2b=3+9

8a+2b=12

8a+2b=12÷(2)=>4a+b=6


p(x)=ax*3-2x*2+bx-1
p(1)=ax.(1)^3-2.(1)^2+b.(1)-1

p(1)=a-2+b-1

p(1)=a+b-3

a+b=3




8a+2b=12
a+b=3

método de Cramer::

|`__8___2__`|
|`__1____1__`|

D=8.(1)-2.(1)

D=8-2

D=6


|`__12___2__`|
|`__3____1__`|

Da=12.(1)-2.(3)

Da=12-6

Da=6

a=Da/D

a=6/6

a=1


a+b=3

b=3-a

b=3-1

b=2

a=1 e b=2

espero ter ajudado!

boa tarde!