Question If 3 is one root of x2 + x + c = 0, find the other root
and the value of c.
The Nature of Roots
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
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
b2 4ac = 0
Then there is only one real root
The function only crosses the x axis at the vertex of the
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
For each of the following quadratics
1. Find the value of the discriminant.
2. Use the value to determine the nature of the
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
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