# Worksheet: Writing a Quadratic Equation given the Roots of Another Quadratic Equation

In this worksheet, we will practice writing a quadratic equation given the roots of another quadratic equation.

**Q2: **

Given that and are the roots of the equation , find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q3: **

Given that and are the roots of the equation , find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q4: **

Given that and are the roots of the equation , find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q5: **

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

- A
- B
- C
- D
- E35

**Q6: **

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

- AThe sum is , and the product is 31.
- BThe sum is , and the product is .
- CThe sum is 27, and the product is 31.
- DThe sum is , and the product is .
- EThe sum is , and the product is 2.

**Q7: **

- A
- B
- C
- D
- E

**Q8: **

The roots of the equation , where , are and . Given that , does ?

- Ayes
- Bno

**Q9: **

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

- A
- B
- C
- D
- E

**Q10: **

What is the product of the roots of the equation ?

- A
- B
- C
- D
- E

**Q11: **

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

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

**Q12: **

Find the sum and the product of the roots of the equation without solving it.

- AThe sum is 33, the product is 39.
- BThe sum is 11, the product is 13.
- CThe sum is , the product is 39.
- DThe sum is , the product is 13.
- EThe sum is 33, the product is 3.

**Q13: **

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

- A
- B
- C
- D
- E10

**Q14: **

Given that each root of the equation is the multiplicative inverse of the other, find all possible values of .

- A3
- B9
- C
- D
- E1

**Q15: **

The sum of the roots of the equation is equal to the product of the roots of the equation . Find the possible values of .

- A1 or
- B3 or
- C or
- D or 6
- E3 or 12

**Q16: **

The product of the roots of the equation is equal to the sum of the roots of the equation . Find the value of .

**Q19: **

- A
- B
- C
- D
- E

**Q20: **

If and are the roots of the equation , find, in its simplest form, the quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q21: **

- A
- B
- C
- D
- E

**Q22: **

- A
- B
- C
- D
- E

**Q23: **

The roots of the equation are and , where . Find the value of , and determine, in its simplest form, the equation whose roots are and .

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

**Q24: **

- A
- B
- C
- D
- E

**Q25: **

- A
- B
- C
- D
- E