The Discriminant 3102.3.31  Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.

Using the Discriminant In the Quadratic Formula, the expression under the radical sign, b2-4ac is called the discriminant! The value of the discriminant can be used to determine the number of real roots for a quadratic equation!

Plug these in the formula! Using the formula! 2x2 + 10x +11 =0 a=2, b=10, c=11 Plug these in the formula! b2 - 4 a c (10)2-4(2)(11) Use your calculator for this step! Therefore the discriminant is 12

How to know how many roots or solutions a quadratic equation has by using the discriminant and looking at a graph y=2x2+x+3 2x2+x+3=0 b2-4ac (1)2-4(2)(3) = -23 If the answer is negative you will have 0 Real roots If the graph does not cross the x-axis you will have 0 roots!

Example x2+6x+9=0 b2-4ac y=x2+6x+9 (6)2-4(1)(9) The answer is 0. When the answer is zero you will have 1 real root! y=x2+6x+9 The graph touches the x-axis in one place. We call this a double root!

Example x2-5x+2=0 b2-4ac (-5)2-4(1)(2) The answer is 17 Since the answer is positive you will have 2 real roots! The graph crosses the x-axis twice!