Complex Numbers And Quadratic Equations question 197
Question: If $ (x+1) $ is a factor of $ x^{4}-(p-3)x^{3}-(3p-5)x^{2} $ $ +(2p-7)x+6 $ , then $ p= $ [IIT 1975]
Options:
A) 4
B) 2
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
If $ (x+1) $ is a factor of $ x^{4}-(p-3)x^{3}-(3p-5)x^{2}+(2p-7)x+6 $ , then by putting $ x=-1 $ , we get $ 1+(p-3)-(3p-5)-(2p-7)+6=0 $
Þ $ -4p=-16\Rightarrow p=4 $ .
BETA
