Find a value or values of k for which the quadratic has a double root.

Question

2x²+3x+k=0

A) k= 9/9

B) k= -9/8

C) k= -8/9

D) k= 9/8

Answer 1

1. this problem uses the technique completing the square
2. 2(x²+3*x/2+some number)+k=some number; need to add the same value to both sides
3. to find that number you divide the linear term by two and then square that number
4. some number=(3/4)²=9/16
5. add 9/8 to both sides to satisfy laws of equality
6. factor the double root
7. 2(x+3/4)²+k=9/8
8. to satisfy double roots k-9/8 must equal 0 so k= 9/8