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Real Function Roots - Advanced Algebra - Practice Problems, Exercises of Calculus

Birla Institute of Technology and ScienceCalculus

This lecture is from Advanced Algebra. Key important points are: Real Function Roots, Polynomial Problems, Complex Equations, Imaginary Roots, Quadratic Equation

Typology: Exercises

2012/2013

Uploaded on 01/31/2013

badsha
badsha ๐Ÿ‡ฎ๐Ÿ‡ณ

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Name___________________
Advanced Algebra Chapter 5-7C Review
Solve each analytically for real and imaginary roots.
1)
2
x 25 0+=
2)
2
2y 36 0+=
3)
2
x 10x 21
โˆ’=โˆ’
4)
2
x 12= โˆ’ 5)
2
3y 12 0
+=
6)
2
x 4x 5+=
7)
2
x 9x 0
8)
2
12x 19x 18 0+ โˆ’=
9)
2
x 20= โˆ’
10)
2
x 8x=
11)
2
6x 31x 35 0โˆ’ +=
12)
2
3x 9=
pf3
pf4
pf5

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Name___________________

Advanced Algebra Chapter 5-7C Review

Solve each analytically for real and imaginary roots.

  1. (^) x 2 + 25 = 0 2) (^) 2y 2 + 36 = 0 3) (^) x^2 โˆ’ 10x = โˆ’ 21

  2. (^) x 2 = โˆ’ 12 5) (^) 3y 2 + 12 = 0 6) (^) x 2 + 4x = 5

  3. (^) x 2 + 9x = 0 8) (^) 12x 2 + 19x โˆ’ 18 = 0 9) (^) x^2 = โˆ’ 20

  4. (^) x 2 = 8x 11) (^) 6x^2 โˆ’ 31x + 35 = 0 12) (^) 3x 2 = 9

  1. (^) y 4 โˆ’ 7y^3 โˆ’18y 2 = 0 14) (^) m 4 โˆ’ 9 = 0

  2. (^) x 3 + 27 = 0 16) (^) 64x 3 โˆ’ = 1 0

Write a quadratic equation in standard form with the given roots.

  1. (^) x 2 โˆ’ 5x + 3 = 0 32) (^) 7x 2 + 6x = โˆ’ 2

Solve each equation.

  1. (^) โˆš๐‘ฅ โˆ’ 3 + 2 = 4 34) ( 5 ๐‘ฆ + 1 )

1 (^3) + 4 = 0

(๐‘ฅ + 7 )

1 (^2) + 5 = 4

  1. (^) โˆš 4 ๐‘ฅ + 1 = โˆš 2 ๐‘ฅ + 7

(๐‘ฅ โˆ’ 3 )

1 (^4) + 1 = 3

  1. (^) โˆš๐‘ฅ + 22 = โˆš๐‘ฅ + 6 + 2

  2. (^) โˆš 6 ๐‘ฅ โˆ’ 5 3

  • 2 = โˆ’ 3 40)^ โˆš๐‘ฅ + 10 + โˆš๐‘ฅ โˆ’ 6 = 8

Solve each inequality. Write your answer in interval notation.

  1. (^) x 2 โˆ’ 7x > 0 42) (^) x 2 โˆ’ 2x โ‰ฅ 15

  2. (^) 2x 2 + 3x + < 1 0 44) (^) 9x 2 โˆ’ 2 โ‰ค3x

Write each function in vertex form. Then graph the parabola.

  1. (^) y > x 2 โˆ’ 8x + 16

Vertex:

  1. (^) y โ‰ค โˆ’ 3x 2 + 6x โˆ’ 1

Vertex: