In this worksheet, we will practice writing a quadratic equation given its roots.

**Q2: **

What is the sum of the roots of the equation ?

**Q3: **

If the roots of the equation are equal, what are the possible values of ?

- A
- B0
- C10
- D
- E

**Q4: **

What is the simplest form of the quadratic equation whose roots are and ?

- A
- B
- C
- D

**Q5: **

Find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q6: **

Find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q7: **

Given that and are the solutions of the equation , find the values of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q8: **

Given that is a root of the equation , determine the value of .

**Q9: **

If one of the roots of the equation is a root of the equation , what is the value of ?

- A
- B or 0
- C0
- D27 or 0

**Q10: **

The sum, , of the first consecutive integers can be found using Starting from 1, how many consecutive integers are required to make a sum of 1,953?

**Q11: **

Find the solution set of in .

- A
- B
- C
- D

**Q12: **

Find the positive number whose square is 12 more than four times the number.

**Q13: **

If and are the roots of the equation , what is the value of ?

**Q14: **

Given that is one of the roots of the equation , find the value of and the value of the other root.

- A , other root
- B , other root
- C , other root
- D , other root

**Q15: **

If the two roots of the equation are equal, determine the value of , then find the two roots.

- A , roots: ,
- B , roots: 1, 1
- C , roots: ,
- D , roots: 1, 1

**Q16: **

Given that a root of the equation is , what is the value of ?

**Q17: **

If and are the roots of the equation , what is the value of ?

**Q18: **

Find the values of for which one of the roots of the equation is the square of the other.

- A , 18
- B384,
- C24,
- D , 162
- E , 27

**Q19: **

Given that 1 and 12 are the roots of the equation , find the values of and .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q20: **

Given that is one of the roots of the equation , find the other root and the value of .

- A ,
- B ,
- C ,
- D ,
- E ,

**Q21: **

Given that is a solution of the equation , find the value of .

**Q22: **

Given that 3 is a solution of the equation , find the value of .

**Q23: **

Without solving the equation , find the sum of its roots.

- A
- B
- C
- D
- E

**Q24: **

Given that and are the roots of the equation , find the value of .

**Q25: **

Given that the sum of the roots of the equation is equal to their product, find the value of .