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Homework: Solving Quadratic Equations

Module by: Kenny M. Felder. E-mail the author

Summary: Some homework problems on solving quadratic equations.

Exercise 1

2x 2 − 5x − 3 = 0 2x 2 − 5x − 3 = 0 size 12{2x rSup { size 8{2} } - 5x - 3=0} {}

  • a. Solve by factoring
  • b. Solve by completing the square
  • c. Solve by using the quadratic formula x=−b±b2−4ac2ax=−b±b2−4ac2a size 12{x= { { - b +- sqrt {b rSup { size 8{2} } - 4 ital "ac"} } over {2a} } } {}
  • d. Which way was easiest? Which way was hardest?
  • e. Check your answers by plugging back into the original equation.

For exercises #2-6, solve any way that seems easiest.

Exercise 2

x 2 − 5x + 30 = 5 ( x + 1 ) x 2 − 5x + 30 = 5 ( x + 1 ) size 12{x rSup { size 8{2} } - 5x+"30"=5 \( x+1 \) } {}

Exercise 3

3x 2 + 24 x + 60 = 0 3x 2 + 24 x + 60 = 0 size 12{3x rSup { size 8{2} } +"24"x+"60"=0} {}

Exercise 4

2 3 x 2 + 8 . 5x = πx 2 3 x 2 + 8 . 5x = πx size 12{ { {2} over {3} } x rSup { size 8{2} } +8 "." 5x=πx} {}

Exercise 5

x 2 − x = 0 x 2 − x = 0 size 12{x rSup { size 8{2} } - x=0} {}

Exercise 6

9x 2 = 16 9x 2 = 16 size 12{9x rSup { size 8{2} } ="16"} {}

Exercise 7

Consider the equation x2+8x+c=0x2+8x+c=0 size 12{x rSup { size 8{2} } +8x+c=0} {} where cc size 12{c} {} is some constant. For what values of cc size 12{c} {} will this equation have…

  • a. Two real answers?
  • b. One real answer?
  • c. No real answers?

Exercise 8

Starting with the generic quadratic equation ax2+bx+c=0ax2+bx+c=0 size 12{ ital "ax" rSup { size 8{2} } + ital "bx"+c=0} {}, complete the square and derive the quadratic formula. As much as possible, do this without consulting your notes.

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