Without solving the equation, determine the nature of the roots of the 1. following equation: x-2=-

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
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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