If x2+ax+b leaves the same remainder 5 when divided by x-1 or x+1 then the value of a and b are respectively
Answers
Answer:
a = 0 ; b = 4
Step-by-step explanation:
let , p(x) = x²+ax+b
given, p(x) / (x-1 ) leaves remainder 5
⇒ p(1) = 5
⇒ 1²+a(1)+b = 5
⇒a+b = 5-1
⇒a+b=4 -------------- I
also p(x) / (x+1) leaves the same remainder 5.
⇒ p(-1) = 5
⇒ (-1)²+a(-1)+b = 5
⇒ 1 - a + b =5
⇒ -a+b = 5-1 = 4
ie., -a+b = 4 ------------------ II
add I and II ,
a + b -a + b = 4 + 4
2b = 8 ⇒ b=4
substitute b=4 in I , we get,
a + 4 = 4 ⇒ a = 4-4 =0
⇒ a = 0
Answer:
a = 0 ; b = 4
Step-by-step explanation:
let , p(x) = x²+ax+b
given, p(x) / (x-1 ) leaves remainder 5
⇒ p(1) = 5
⇒ 1²+a(1)+b = 5
⇒a+b = 5-1
⇒a+b=4 -------------- I
also p(x) / (x+1) leaves the same remainder 5.
⇒ p(-1) = 5
⇒ (-1)²+a(-1)+b = 5
⇒ 1 - a + b =5
⇒ -a+b = 5-1 = 4
ie., -a+b = 4 ------------------ II
add I and II ,
a + b -a + b = 4 + 4
2b = 8 ⇒ b=4
substitute b=4 in I , we get,
a + 4 = 4 ⇒ a = 4-4 =0
⇒ a = 0