Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![CONSOLIDATION EXERCISE (NATURE OF ROOTS)
28/04/21
1.
Without solving the equation, determine the nature of the roots of the
following equation: x-2=-
2.
Determine the nature of the roots of the following equation:
ax + (a+1)x=-1 where a 1; a # 0
3.
If x -4 is a root of 2x-rx+12 =0, find the value of r and the other root.
4.
Prove that the roots of p'x + pqx+ q° = 0 are non-real if p and g are real
with p+0 and q + 0.
5.
Show that the roots of the equation mx+5x-m =0 are real and unequal
for all real values of m. (m * 0)
6.
29/04 /21
Given:
2x + (2k – 1)x –k = 0
6.1
Prove that the roots of this equation will be rational for all rational valu
of k.
6.2
For what value(s) of k will the roots be equal ?
7.
For what value(s) of kwill the roots of kx +(2k – 1)x+k = 0 be equal ?
x² -4x+k = 0
8.
8.1
Given:
For what values of k will the roots of the equation be real ?
Find one integral value of k (k* 0) for which the equation will have rational
roots.
8.2
9.
Give the equation with roots 3 and - 4 in the form a? +bx +c = 0.
The roots of a quadratic equation are 2+v16-4t2. Determine the value(s) of
t for which the roots will be equal.
10.
4
Find the values of
11.
The roots of the equation 3x² – bx+c = 0 are -2 and-
b and c.
301
The discriminants of the equations 4x-x+p= 0 and 2x² – 4x + 5 = 0 are equal to
one another. Determine the value(s) of p.
12.
Given:
px-6x+(p+8) = 0 v
13.
13.1 Show that the discriminant A = 36-32p-4p.
13.2 Determine p if the roots are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facf0f5cd-5c13-4edb-b84c-be1d62fa8d40%2F2705c4a2-92ac-40ba-a8c4-f342f73aa315%2F8o3gdf9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:CONSOLIDATION EXERCISE (NATURE OF ROOTS)
28/04/21
1.
Without solving the equation, determine the nature of the roots of the
following equation: x-2=-
2.
Determine the nature of the roots of the following equation:
ax + (a+1)x=-1 where a 1; a # 0
3.
If x -4 is a root of 2x-rx+12 =0, find the value of r and the other root.
4.
Prove that the roots of p'x + pqx+ q° = 0 are non-real if p and g are real
with p+0 and q + 0.
5.
Show that the roots of the equation mx+5x-m =0 are real and unequal
for all real values of m. (m * 0)
6.
29/04 /21
Given:
2x + (2k – 1)x –k = 0
6.1
Prove that the roots of this equation will be rational for all rational valu
of k.
6.2
For what value(s) of k will the roots be equal ?
7.
For what value(s) of kwill the roots of kx +(2k – 1)x+k = 0 be equal ?
x² -4x+k = 0
8.
8.1
Given:
For what values of k will the roots of the equation be real ?
Find one integral value of k (k* 0) for which the equation will have rational
roots.
8.2
9.
Give the equation with roots 3 and - 4 in the form a? +bx +c = 0.
The roots of a quadratic equation are 2+v16-4t2. Determine the value(s) of
t for which the roots will be equal.
10.
4
Find the values of
11.
The roots of the equation 3x² – bx+c = 0 are -2 and-
b and c.
301
The discriminants of the equations 4x-x+p= 0 and 2x² – 4x + 5 = 0 are equal to
one another. Determine the value(s) of p.
12.
Given:
px-6x+(p+8) = 0 v
13.
13.1 Show that the discriminant A = 36-32p-4p.
13.2 Determine p if the roots are equal.
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