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?
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
Q10:
Which of the following describes the roots of the equation ?
- Areal and different
- Bcomplex and not real
- Creal and equal
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
Q19:
What type of roots does the equation have for all real values of ?
- Acomplex numbers
- Breal and different
- Creal and equal
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