# Worksheet: Properties of a Discriminant in a Quadratic Equation

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?

**Q4: **

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

- Arational
- Bnot rational

**Q5: **

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

- A The discriminant is equal to zero.
- B The discriminant is positive.
- C The discriminant is negative.
- D The discriminant is nonnegative.
- 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

**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 following equation have?

- Ano roots
- Bone root
- Cinfinite number of roots
- Dtwo 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 ?

- 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: **

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
- C12
- D

**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 equal
- Creal and different

**Q20: **

Determine the type of the roots of the equation .

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

**Q21: **

Determine the type of the roots of the equation .

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

**Q22: **

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

- Ayes
- Bno

**Q23: **

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

**Q24: **

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

- Ayes
- Bno

**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 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