If x+2 is a factor of …
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Posted by Arnav Yadav 4 years, 3 months ago
- 4 answers
Gaurav Seth 4 years, 3 months ago
Let given polynomial p(x)=ax³+bx²+x-6 ,
i) If x+2 is a factor of p(x) then
p(-2) = 0
By factor theorem
a(-2)³+b(-2)²+(-2)-6=0
=> -8a+4b-8=0
Divide each term by 4 , we get
=> -2a+b-2 =0
=> -2a+b = 2 ---(1)
ii) If p(x) divided by (x-2) the remainder is p(2)
According to the problem given,
p(2) = 4
=> a(2)³+b(2)²+2-6=4
=> 8a+4b-4=4
Divide each term by 4, we get
=> 2a+b-1=1
=> 2a+b=2 ---(2)
Add equation (1) and (2) , we get
2b = 4
Substitute b = 2 , in equation (2) ,we get
2a+2=2
=> 2a = 2-2
=> 2a = 0
=> a = 0
Therefore,
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Madhav Manroa 4 years, 3 months ago
0Thank You