Solve each of the following equations:
Question 1: where
Answer:
where
Question 2:
Answer:
Question 3:
Answer:
Question 4:
Answer:
Multiplying the equation by 8.
Question 5:
Answer:
Question 6:
Answer:
Let
When
When
Question 7:
Answer:
Let
When ,
is imaginary
When , then
Question 8:
Answer:
Let
Therefore
When
When
Therefore
Question 9:
Answer:
When
When
Question 10:
Answer:
Let
When
When
Question 11:
Answer:
Let
When
When
is imaginary
Question 12: [2005]
Answer:
Comparing with
, we get
Since
Therefore
Solving we get
Question 13: [2004]
Answer:
Comparing with
, we get
Since
Therefore
Solving we get
Question 14:
Answer:
Let
When
When
Question 15:
Answer:
Since
Question 16:
Answer:
Question 17:
Answer:
Question 18:
Answer:
Let
When
When
Question 19:
Answer:
Question 20:
Answer:
Question 21:
Answer:
Find so that the equation have equal roots:
Question 22:
Answer:
Comparing with
, we get
For roots to be equal, we should have
Solution:
Question 23:
Answer:
Comparing with
, we get
For roots to be equal, we should have
Solving the equation
Question 24:
Answer:
Comparing with
, we get
For roots to be equal, we should have
When
When
Question 25: [2010]
Answer:
Comparing with
, we get
For roots to be equal, we should have
Question 26: [2012]
Answer:
Comparing with
, we get
For roots to be equal, we should have