# Worksheet: Writing a Quadratic Equation given the Roots

Q1:

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

• A
• B
• C
• D
• E

Q2:

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

Q3:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q4:

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

Q5:

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

Q6:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q7:

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

• A ,
• B ,
• C ,
• D ,
• E ,

Q8:

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 1β953?

Q9:

Find the solution set of in .

• A
• B
• C
• D

Q10:

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

Q11:

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

Q12:

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

Q13:

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

• A
• B
• C
• D
• E

Q14:

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

Q15:

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

• A
• B
• C
• D
• E

Q16:

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

Q17:

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

Q18:

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

• A
• B
• C
• D

Q19:

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

• A
• B
• C
• D

Q20:

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

Q21:

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

• A
• B
• C
• D

Q22:

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

Q23:

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

Q24:

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

• A
• B
• C
• D
• E

Q25:

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

• A
• B
• C
• D
• E