1. 1. Find the solution to 1. Find a quadratic equation given that the sum of its roots is 7 and the product of its roots is 1 2. Find a quadratic equation whose solutions are and.

3.  Solve equations that are reducible to quadratic form  Solve real world problems using algebraic reasoning skills.

4.  This problem was found in the writings of the Hindu mathematician Mahavira. One fourth of a herd of camels was seen in the forest, twice the square root of the number of camels in the herd had gone to the mountain slope, and three times five camels were found to remain on the bank of a river. What is the numerical measure of that herd of camels.  The equation, which models Mahavira’s situation is not quadratic. However, a substitution for x, we get a quadratic equation.  Such equations are said to be reducible to quadratic form. To solve such equations, we first make a substitution and solve for the new variable. Then we substitute back the original variable and solve again.

5. Solve Let. Then we solve the equation found by substituting u for or Now we substitute for u and solve these equations. u = 8 or u = 1 or These four numbers check. The solutions are 1,-1,,

6. Solve Let. Then we solve the equation found by substituting u for Squaring the first equation we get x = 16. The second equation has no solution since principle square roots are never negative. The number 16 checks and is the only solution. u = 4 or u = -1 or Substituting for u

7. Solve 1. 2. 3.

8. Solve Let. Then we solve the equation found by substituting u for The numbers and and 0 check. They are the solutions. u = 2 or u = -1 Now we substitute for u or

9. Solve

10. Let. Then we solve the equation found by substituting u for The numbers 32 and -1check. They are the solutions. u = 2 or u = -1 Now we substitute for u or

11. Solve 1. 2.