Quadratic Equations
Exercises for students:
(1) Show that x2 + 6x + 8 = 0 has 2 distinct real roots.
(2) Show that x2 + 6x + 9 = 0 has equal roots.
(3) Show that x2 + 6x + 10 > 0 for all real x.
(3) Show that -x2 + 6x - 10 < 0 for all real x.
Complete the square for the following quadratic expressions on paper and check your working using the above applet:
(4) x2 + 2x + 2
(5) x2 + 6x + 2
(6) x2 - 6x + 2
(7) x2 + 5x + 2
(8) 2x2 + 5x + 2
(9) -x2 + 5x + 2
Summary
ax2 + bx + c = 0 has
- 2 distinct real roots if b2 - 4ac > 0
- equal real roots if b2 - 4ac = 0
- no real roots if b2 - 4ac < 0
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