Homework Help: How do I calculate these questions relating to roots of quadratic equation?

1. Jan 28, 2010

eureka_beyond

1. The problem statement, all variables and given/known data
These two questions are very similar:
1) Let c be a constant. If a and b are the roots of the equation x^2 + 2x - c = 0
then 2b-a^2 = ?

2) Let k be a constant. If a and b are the roots of the equation x^2 - 3x + k = 0
Then a^2 + 3b = ?

2. Relevant equations
The answer to these 2 questions are -4-c and 9-k.

3. The attempt at a solution
For the first one, I was thinking about using the sum of roots and product of roots, I know that a+ b is -2 and ab must be c, but I don't know how to convert 2b-a^2 in to a new equation that only consists of a+b and ab . I used another approach, which is to turn the equation into 2 seperate ones by knowing the two roots given, a^2 + 2a - c = 0 and b^2 + 2b - c = 0. Then after some change of subject, I'll know that a^2 = c-2a and 2b = c-b^2 . But if I put in these two together, 2b-a^2 will equal to c-(b^2)-c+2a, which will finally give 2a-b^2, which doesn't really solve the problem....
I thought of another way, which is to let those unknowns to be a random number. Since this is a multiple choice question, I can get the answer by try and error. However, I was thinking if there's a better way.
Thanks

2. Jan 28, 2010

Dick

Your first approach was right. a+b=(-2). So b=(-2)-a. 2b-a^2=2(-2-a)-a^2=(-4)-(2a+a^2). Now finish up.