Find the value of p for which ( X+p) is a factor of. X2+px+3+p
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Answered by
12
f(x)= x²+px+3+p
If (x+p) is a factor, by factor theorem,
(x+p)=0
⇒x= -p
∴f(-p) =0
∴f(-p)=(-p)²+p(-p) +3+p =0
⇒3+p = 0
⇒p = 3
If (x+p) is a factor, by factor theorem,
(x+p)=0
⇒x= -p
∴f(-p) =0
∴f(-p)=(-p)²+p(-p) +3+p =0
⇒3+p = 0
⇒p = 3
Answered by
1
Step-by-step explanation:
If x+2 is a factor of f(x) then
f(−2)=0
∴2(−2)
3
+p(−2)
2
+(−2)−10=0
4p=12+16
p=7
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