Solve each of the following use quadratic formula

Question 1:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 2:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 3:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 4:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 5:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 6:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 7:

Answer:

Multiplying by 6

or

Comparing with , we get

Since

Therefore

Solving we get

Question 8:

Answer:

Multiplying by 15 and simplifying we get

or

Comparing with , we get

Since

Therefore

Solving we get

Question 9:

Answer:

or

Comparing with , we get

Since

Therefore

Solving we get

Question 10:

Answer:

or

Comparing with , we get

Since

Therefore

Solving we get

Question 11:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 12:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 13:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Question 14:

Answer:

Comparing with , we get

Since

Therefore

Solving we get

Without solving, comment on the roots of each of the equations

*Notes: The nature of the roots depends on the value of the . Also in the equation , are real and . The following cases can happen:*

*i) : In this case the roots would be real and equal.*

*ii) : In this case the roots would be real and unequal.*

*iii) : In this case the roots would be imaginary numbers*

Question 15:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and unequal.*

Question 16:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and unequal.*

Question 17:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and equal*

Question 18:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and unequal*

Question 19:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and unequal*

Question 20:

Answer:

Comparing with , we get

Therefore

Hence since *: In this case the roots would be real and unequal*

Find the value of if the quadratic equations have equal roots:

Question 21:

Answer:

Comparing with , we get

For roots to be equal, we should have

Substituting

Question 22:

Answer:

Comparing with , we get

For roots to be equal, we should have

Substituting

Question 23:

Answer:

Comparing with , we get

For roots to be equal, we should have

or

Question 24:

Answer:

Comparing with , we get

For roots to be equal, we should have