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