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The discriminant of a quadratic formula

The discriminant of a quadratic formula. IB SL/HL www.ibmaths.com. Use your GDC to find which of the following have either: no solutions, 1 repeated solution, or 2 solutions. 1. 2 solutions. 2. 0 solutions. 3. 2 solutions. 4. 1 solution. 5. 0 solutions. 6. 1 solution.

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The discriminant of a quadratic formula

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  1. The discriminant of a quadratic formula • IB SL/HL • www.ibmaths.com

  2. Use your GDC to find which of the following have either: no solutions, 1 repeated solution, or 2 solutions. 1. 2 solutions 2. 0 solutions 3. 2 solutions 4. 1 solution 5. 0 solutions 6. 1 solution Which part of the quadratic equation determines the number of solutions of a quadratic? Now use the quadratic formula to verify your results.

  3. You should have now found the following facts: 2 solutions 1 repeated solution 0 solutions

  4. Using the discriminant to solve typical examination questions 1 As there is 1 repeated solution use the highlighted formula. Find the value(s) of k in the following quadratic given the quadratic has 1 repeated solution.

  5. Using the discriminant to solve typical examination questions 2 As there are 2 solutions use the highlighted formula Find the range of values for k in the following quadratic given the quadratic has 2 solutions. and Be careful with the negative answer, and the change of sign.

  6. Using the discriminant to solve typical examination questions 3 As there are 0 solutions use the highlighted formula. Find the range of values for k in the following quadratic given the quadratic has 0 solutions. and Again, be careful with the negative answer, and the change of sign.

  7. 1. Show that the equation has no real solutions if

  8. 2. Show that if or then has two equal solutions.

  9. 3.Show that if the line touches the parabola with equation then k = -1 or k = 15.

  10. 4. Show that the graphs of the functions and touch, and find the coordinates of their point of contact.

  11. 5. Find the values of k for which touches . Find also the coordinates of the point where they touch.

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