# Worksheet: Forming a Quadratic Equation from its Roots

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

Q1:

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

• A
• B
• C
• D
• E

Q2:

What is the sum of the roots of the equation ?

Q3:

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

• A
• B
• C
• D

Q4:

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

• A
• B
• C
• D
• E

Q5:

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

• A,
• B,
• C,
• D,
• E,

Q6:

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

Q7:

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

• A or 0
• B
• C27 or 0
• D0

Q8:

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

Q9:

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

Q10:

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

Q11:

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

Q12:

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

• A24,
• B, 18
• C, 27
• D, 162
• E384,

Q13:

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

• A,
• B,
• C,
• D,
• E,

Q14:

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

Q15:

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

Q16:

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

• A
• B
• C
• D
• E

Q17:

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

Q18:

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

Q19:

What is the product of the roots of the quadratic equation ?

• A
• B
• C
• D

Q20:

If the sum of the roots of the equation is 4, what is the value of ?

Q21:

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

Q22:

The difference between the roots of the equation is . What is the value of ?

Q23:

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

• Ano
• Byes

Q24:

If the product of the roots of the equation is , what is the value of ?

Q25:

The roots of the equation are positive numbers which are in the ratio . What is the value of ?

• A
• B72
• C26
• D