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Byju's Answer
Standard X
Mathematics
Division Algorithm for a Polynomial
Find p and q ...
Question
Find p and q such that (x + 1 ) and (x - 1) are factors of the polynomial,
x
4
+
p
x
3
−
3
x
2
+
2
x
+
q
find the values of a and b so that the polynomial
x
3
−
a
x
2
−
13
x
+
b
has
(
x
−
1
)
and
(
x
+
3
)
as factors.
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Solution
x
4
+
p
x
3
−
3
x
2
+
2
x
+
2
If (x-1) & (x+1)are the factor
λ
then they will satisfy if.
x-1 = 0, x+1 = 0
x = 1 & x = -1
Let x = 1 & x = -1
1
+
p
−
3
+
α
+
q
=
0
p
+
2
=
0
__ (1)
1
−
p
−
3
−
α
+
2
=
0
−
p
+
q
=
4
__ (2)
add both
2
q
=
4
q
=
2
p
=
−
2
ii)
x
3
−
a
x
2
−
13
x
+
b
if (x-1) & (x+3) are factor
then they will satisfied it.
put x = 1 & x = -3
1
−
a
−
13
+
b
=
0
−
a
+
b
=
12
__ (1)
−
27
−
9
a
+
39
+
b
=
0
b
=
9
a
−
12
Suggest Corrections
1
Similar questions
Q.
If
x
+
1
&
x
−
1
are factors of polynomial
x
4
+
p
x
3
−
3
x
2
+
2
x
+
q
then find the value of
P
&
Q
.
Q.
Find the values of
a
and
b
so that the polynomial
x
3
+
a
x
2
−
13
x
+
b
has
x
−
1
and
x
−
3
as factors.
Q.
Find the values of a and b so that the polynomials
x
3
−
a
x
2
−
13
x
+
b
has (x - 1) and (x + 3) as factors.
Q.
Find the value of
p
and
q
such that
(
x
+
1
)
and
(
x
+
2
)
are the factors of
x
4
+
p
x
3
+
2
x
2
−
3
x
+
q
.
Q.
Find the values of a and b so that(x-1) and (x+1) are the factors of x
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3
-3x
2
+2x+b
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