11. If x+2 is a factor of f(x)=
x^2+px+2qand p+q=4, then *
2 points
x2 + px + 29
O p=1, q=3
O p=3,q=1
O p=-1,9=5
O p=5,q=-1
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Answer:
Let α be the common root
∴α
2
+pα+q=0 ...........(1)
and α
2
+qα+p=0 ........ (2)
Solving (1) & (2), we get,
p
2
−q
2
α
2
=
q−p
α
=
q−p
1
∴α=
q−p
p
2
−q
2
and α=1
⇒
q−p
p
2
−q
2
=1
⇒p
2
−q
2
=q−p
(or) (p
2
−q
2
)+(p−q)=0
⇒(p−q)[p+q+1]=0
⇒p−q=0 or p+q+1=0
Step-by-step explanation:
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