# Worksheet: Discriminants of Quadratics

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.

- 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

**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