# Lesson Worksheet: Discriminants of Quadratics Mathematics

In this worksheet, we will practice finding the discriminant of a quadratic equation and using it to determine the number and type of its roots (solution) without solving it.

Q1:

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

Q2:

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

Q3:

Determine the type of the roots of the equation .

• Areal and different
• Breal and equal
• Ccomplex and not real

Q4:

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

• Anot rational
• Brational

Q5:

Which is the correct condition for the quadratic equation with real coefficients to have no nonreal roots?

• AThe discriminant is positive.
• BThe discriminant is nonnegative.
• CThe discriminant is equal to zero.
• DThe discriminant is negative.
• EThe discriminant is an integer.

Q6:

The roots of the equation have different signs. Find the interval in which lies.

• A
• B
• C
• D
• E

Q7:

If the roots of the equation are not real, find the interval which contains .

• A
• B
• C
• D

Q8:

How many real roots does the equation have if and ?

Q9:

Determine the type of the roots of the equation .

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

Q10:

Which of the following describes the roots of the equation ?

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

Q11:

How many real roots does the equation have?

• AInfinite number of roots
• BOne root
• CTwo roots
• DNo roots

Q12:

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

Q13:

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

• ANo
• BYes

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: 2, 2, or , roots: ,
• B, roots: , , 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:

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

• A
• B
• C
• D
• E

Q17:

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

• A
• B
• C
• D12

Q18:

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

• A
• B
• C
• D

Q19:

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

• Acomplex numbers
• Breal and different
• Creal and equal

Q20:

Determine the type of the roots of the equation .

• Areal and equal
• Breal and different
• Ccomplex and not real

Q21:

Determine the type of the roots of the equation .

• Areal and different
• Breal and equal
• Ccomplex and not real

Q22:

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

• ANo
• BYes

Q23:

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

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

Q24:

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

• ANo
• BYes

Q25:

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 and 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 2 and 2 or , the two roots are and
• D, the two roots are 2 and 2 or , the two roots are and