1. Question­ If ­3 is one root of x2 + x + c = 0, find the other root
and the value of c.
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2. The Discriminant
The Nature of Roots
b2 ­ 4ac
­From the quadratic formula is known as the discriminant.
­It allows us to determine if the roots are real or imaginary.
­If the roots are real it also allows us to determine if there are one or two
roots.
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3. b2 ­ 4ac > 0
There are two roots
If b2 ­ 4ac is a perfect square the roots are rational
If b2 ­ 4ac is not a perfect square the roots are
irrational
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4. b2 ­ 4ac = 0
­Then there is only one real root
­The function only crosses the x axis at the vertex of the
parabola
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5. b2 ­ 4ac < 0
­The roots of the quadratic function are imaginary
­The parabola does not cross the x axis at any point
­There are still imaginary roots to the function
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6. For each of the following quadratics
1. Find the value of the discriminant.
2. Use the value to determine the nature of the
roots.
3. Use to quadratic formula to find the exact
value for the roots of each quadratic.
4. Draw a very rough sketch of what the quadratic might
look like.
a) x2 ­ x ­12 = 0
b) ­x2 + 2x + 18 = 0
c) x2 ­ x + 2 = 0
d) ­x2 + x ­ 4 = 0
e) x2 ­ 6x + 9 = 0
f) ­x2 + 10x ­25 = 0
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7. a) x2 ­ x ­12 = 0
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8. b) ­x2 + 2x + 18 = 0
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9. c) x2 ­ x + 2 = 0
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10. d) ­x2 + x ­ 4 = 0
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11. e) x2 ­ 6x + 9 = 0
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12. f) ­x2 + 10x ­25 = 0
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