(adsbygoogle = window.adsbygoogle || []).push({}); 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

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

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