Complex Numbers And Quadratic Equations question 807
Question: The roots of the equation $ x^{4}-4x^{3}+6x^{2}-4x+1=0 $ are [MP PET 1986]
Options:
A) 1, 1, 1, 1
B) 2, 2, 2, 2
C) 3, 1, 3, 1
D) 1, 2, 1, 2
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ f(x)=x^{4}-4x^{3}+6x^{2}-4x+1=0 $
Þ $ (x-1)(x^{3}-3x^{2}+3x-1)=0 $
Þ $ (x-1){{(x-1)}^{3}}=0 $
Þ $ x=1,1,1,1 $
BETA
