Find the value of p(1) of the polynomial p(x) =x2+7×-6
Answers
Answer:
P(1) means to replace 1 in place of x
that is :
1²+7(1)-6
=1+7-6
2
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Asked on December 26, 2019 by
Md Bhargava
Find the values of a and b so that the polynomial p(x)=x
2
+x
3
+8x
2
−ax+b is exactly divisible by x
2
−1.
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ANSWER
We have,
p(x)=x
4
+x
3
+8x
2
−ax+b
x
2
−1=0
x
2
=1
x=±1
Since, polynomial p(x) is exactly divisible by x=±1.
⇒p(1)=0
⇒p(−1)=0
Put x=1, then
1
4
+1
3
+8(1)
2
−a(1)+b=0
1+1+8−a+b=0
10−a+b=0
a−b=10 .........(1)
Put x=−1, then
(−1)
4
+(−1)
3
+8(−1)
2
−a(−1)+b=0
1−1+8+a+b=0
8+a+b=0
a+b=−8 .........(2)
Add equations (1) and (2), we get
a−b=10
a+b=−8
2a+0=2
2a=2
a=1
Subtract equation (1) and (2), we get
a+b=−8
a−b=10
0+2b=−18
2b=−18
b=−9
∴ a=1,b=−9
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