1
x^2 + 2ax + a^2 - 4 = 0
Chapter 23 · Quadratic Equations
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From Quadratic Equations with Literal Coefficients, exercise 3
Solve for x by completing the square, and check:
From Problems Leading to Quadratics, exercise 2
Reject all answers which do not satisfy the conditions of the problems. Where two answers both satisfy a problem, give both.
2
Find two numbers whose difference is 11 and whose product is 42.
From Solution by Formula, exercise 4
Solve for x by formula, and check:
3
2x + 2 = x^2
From Solution by Completing the Square, exercise 20
Solve by completing the square, and check results:
4
25x^2 - 20x - 12 = 0
From Solution by Completing the Square, exercise 18
Solve by completing the square, and check results:
5
20s^2 + s = 1
From Geometrical Problems, exercise 7
Use the figures in the lesson.
6
In the figure of the two chords, AC = 18, DB = 4, and BE = 20. Find AB.
From Solution by Completing the Square, exercise 7
Solve by completing the square, and check results:
7
t^2 - 2t - 15 = 0
From Problems of Rate, Work, and Falling Bodies, exercise 27
Reject all answers which do not satisfy the conditions of the problems.
8
Two pumps together can fill a standpipe in 45 minutes. One pump alone requires 2 hours less time than the other. Find the time each requires alone.
From Quadratic Equations with Literal Coefficients, exercise 11
Solve for x by completing the square, and check:
9
a^2x^2 + 2ab = a^2 + b^2
From Harder Equations; Equations in the Quadratic Form, exercise 44
Solve these equations in the quadratic form (each has four roots):
10
4k^4 = 9k^2 - 2