Learning Resources

Investigation 6: The Number of Roots of a Quadratic Equation

Test yourself

Use the discriminant to determine the nature of the roots:

1. For the equation 2x² -12x + 18 =0:
   
   a = 2 , b = -12 , c = 18, so:
   
   D=(-12)² - 4(2)(18) = 144 - 144 = 0
   
   Therefore there are two equal real roots (a double root)
   
   

2. 2x² -12x + 19 =0
   
   a = 2 , b = -12 , c = 19, so:
   
   D = (-12)² - (4)(2)(19) = 144 - 152 = -8
   
   Therefore there are no real roots ( there are two complex roots)
   
   

3. 2x² -12x + 15 = 0
   
   a = 2 , b = -12 , c = 15, so:
   
   D = (-12)² - (4)(2)(15) = 144 - 120 = 24
   
   
   Therefore there are two unequal real roots.

If you want a good review of the concepts in this section, solve each of the above equations and verify what the the discriminant told you. Then graph the corresponding function and check its x-intercepts against the roots and against what the discriminant told you.