p(x) =X2 -5x+6 ÷(x-2)
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Answer:
p(x) =X2 -5x+6 ÷(x-2)
Step-by-step explanation:
(a)
P(x)=
x 2
6x+
9
⇒
P(3)=
3 2
6(3)+
9=
9−
18+
9=
0
(b)
P(x)=
x 2
6x+
9=
x 2
6x+
9=
−2×
3×
x+
3 2
(x−3) 2
, which is a perfect square, therefore the number will always be positive
Hence, the value of this polynomial cannot be a negative number.
(c)
P(a)=
a 2
6a+
9
P(b)=
b 2
6b+
9
P(a)+
P(b)
⇒
a 2
6a+
9=
b 2
6b+
9
⇒
a 2
b 2
6a+
6b=
0
⇒
(a
2
−b
2
) −
6(a−
b)=
0
⇒
(a−
b)(a+
b)−
6(a−
b)=
0
⇒
(a−
b)(a+
b−
6)=
0
⇒
(a−
b)=
0⇒
a=
b
(Not possible)
a+
b=
6
There can be many numbers as long it satisfies
a+
b=
6
For example,
a=
1,b=
5
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