Remember to show all work and use correct notation to earn full credit.

1.Solve the following quadratic equation for x: 2x 2 − 5x + 7 = 0

2. Among all pairs of numbers whose difference is 28, find the pair whose product is minimum. What is the minimum product?

3. (a)  Solve the following quadratic equation for x: x 2 − 7x + 10 = 0 (b) (4 points) Use your answer from part (a) to help solve the following quadratic inequality: x 2 − 7x + 10 ≥ 0 • Sketch a graph of your solution on a horizontal number line. • Express your solution using interval notation.

4. Solve the following radical equation for x: √ 17 − x − 3 = x Remember to check your solutions! If there are no solutions, state NO SOLUTIONS.

5.  Solve the following rational equation for x: 1 x − 6 + x x − 2 = 4 x 2 − 8x + 12 Hint: Factor the quadratic denominator. Remember to check your solutions! If there are no solutions, state NO SOLUTIONS.