# Worksheet: Properties of a Discriminant in a Quadratic Equation

Q1:

Determine the type of the roots of the equation .

• Areal and different
• Bcomplex and not real
• Creal and equal

Q2:

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

Q3:

Given that the roots of the equation are real and different, find the interval which contains .

• A
• B
• C
• D
• E

Q4:

Does the equation have real roots for all real values of ,, and ?

• Ayes
• Bno

Q5:

How many real roots does the following equation have?

• Ano roots
• Bone root
• Cinfinite number of roots
• Dtwo roots

Q6:

Suppose the two roots of the equation are equal. Determine all possible values of , and then find the two roots.

• A , two roots: 3 and 3 or , two roots: and
• B , two roots: 3 and 3 or , two roots: and
• C , two roots: and or , two roots: and
• D , two roots: 3 and 3 or , two roots: and
• E , two roots: and or , two roots: and

Q7:

How many non-real roots will a quadratic equation have if its discriminant is negative?

Q8:

Which of the following describes the roots of the equation ?

• Areal and different
• Bcomplex and not real
• Creal and equal

Q9:

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

Q10:

Determine whether the roots of the equation are rational or not without solving it.

• Arational
• Bnot rational

Q11:

Given that and are rational, non zero numbers, are the roots of the equation always rational?

• Ayes
• Bno

Q12:

If the roots of the equation are equal, what are the possible values of ? For each value of , work out the roots of the equation.

• A , the two roots are 2 and 2 or , the two roots are and
• B , the two roots are 2 and 2 or , the two roots are and
• C , the two roots are and or , the two roots are and
• D , the two roots are 2 and 2 or , the two roots are and

Q13:

Are the roots of the equation rational for all rational values of ?

• Ayes
• Bno

Q14:

Given that the roots of the equation are equal, determine all possible values of . For each value of , work out the roots of the equation.

• A , roots: , , or , roots: ,
• B , roots: 2, 2, or , roots: ,
• C , roots: , , or , roots: ,
• D , roots: 2, 2, or , roots: ,

Q15:

Given that is a real number, and the equation does not have real roots, find the interval which contains .

• A
• B
• C
• D
• E

Q16:

Determine the type of the roots of the equation .

• Areal and different
• Bcomplex and not real
• Creal and equal

Q17:

If the roots of the equation are equal, find the possible values of .

• A
• B
• C
• D
• E

Q18:

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

• A
• B
• C12
• D

Q19:

For what value of does the equation have exactly one solution?

• A
• B
• C10
• D
• E

Q20:

Given that the equation has no real roots, find the interval that contains .

• A
• B
• C
• D

Q21:

What type of roots does the equation have for all real values of ?

• Acomplex numbers
• Breal and equal
• Creal and different

Q22:

Determine the type of the roots of the equation .

• Acomplex and not real
• Breal and different
• Creal and equal

Q23:

Determine whether the roots of the equation are rational or not without solving it.

• Anot rational
• Brational

Q24:

Determine the type of the roots of the equation .

• Areal and different
• Bcomplex and not real
• Creal and equal

Q25:

How many non-real roots will a quadratic equation have if its discriminant is positive?