The Discriminant & Nature of Roots: Full Guide — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 11 · Equations

The Discriminant & Nature of Roots: Full Guide

EXAM-STYLE CLASS TEST

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
The DISCRIMINANT of ax² + bx + c = 0 is …
(1)
A)b² − 4ac
B)b² + 4ac
C)−b² − 4ac
D)√(b² − 4ac)
1.2
If Δ > 0 AND Δ is a perfect square, the roots are …
(1)
A)real, rational and unequal
B)real, irrational and unequal
C)real and equal
D)non-real
1.3
If Δ = 0, the roots are …
(1)
A)real and equal
B)real and unequal
C)non-real
D)one real and one non-real
1.4
For x² − 6x + 9 = 0, the roots are …
(1)
A)real and equal
B)real and unequal
C)non-real
D)rational and unequal
1.5
For 2x² + 3x + 5 = 0, the roots are …
(1)
A)non-real
B)real and equal
C)real and rational
D)real and irrational
1.6
For x² − 5x + 3 = 0, the roots are …
(1)
A)real, irrational and unequal
B)real, rational and unequal
C)real and equal
D)non-real
1.7
For which value(s) of k does x² + kx + 4 = 0 have EQUAL roots?
(1)
A)k = 4 or k = −4
B)k = 4 only
C)k = 16
D)k = 2
1.8
If Δ < 0, the graph of the quadratic …
(1)
A)does not cut the x-axis
B)touches the x-axis once
C)cuts the x-axis twice
D)lies entirely below the x-axis
1.9
For 3x² − 12x + 12 = 0, Δ = …
(1)
A)0
B)144
C)288
D)−144
1.10
For which values of k does x² + 2x + k = 0 have REAL roots?
(1)
A)k ≤ 1
B)k ≥ 1
C)k < 1
D)k = 1

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[9 MARKS]

Use the discriminant Δ = b² − 4ac to answer the questions below.

2.1
Describe the nature of the roots of x² − 4x + 4 = 0.
(3)
2.2
Describe the nature of the roots of x² + 3x + 5 = 0.
(3)
2.3
Describe the nature of the roots of 2x² − 7x + 3 = 0.
(3)

Question 3

[14 MARKS]

Answer the questions below.

3.1
Determine the value(s) of k for which kx² + 4x + 2 = 0 has REAL roots.
(5)
3.2
Determine the value(s) of p for which x² + px + 9 = 0 has equal roots.
(4)
3.3
State what the discriminant tells you about the GRAPH of y = ax² + bx + c.
(3)
3.4
Explain the difference between roots that are RATIONAL and roots that are IRRATIONAL.
(2)

TOTAL: 33 marks

This question paper consists of 3 questions.