SOLUTION: If 1/4 and -7/2 are the roots of the quadratic equation Ax2+By+C=0, what is the value of B.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If 1/4 and -7/2 are the roots of the quadratic equation Ax2+By+C=0, what is the value of B.      Log On


   

Question 1183641: If 1/4 and -7/2 are the roots of the quadratic equation Ax2+By+C=0, what is the value of B.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x-(1/4)=0
so (4x-1) is a factor.
Similarly, (2x+7) is a factor.
I am assuming you mean Ax^2+Bx+C=0
so 8x^2+26x-7=0
graph%28300%2C300%2C-5%2C5%2C-50%2C50%2C8x%5E2%2B26x-7%29
B=26

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

As the problem is worded,  IT  HAS  NO  A  UNIQUE  ANSWER  for  B.

From the given data,  you  ONLY  can determine the ratio   B%2FA,  which,  according to  Vieta's theorem,

is the sum of the roots   B%2FA = 1%2F4 + %28-7%2F2%29 = 1%2F4+-+14%2F4 = -13%2F4.

But you can say  NOTHING  about  B  itself,  because you don't know the value of A.


As the problem is given,  it is a   F A K E.


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MEMORIZE  it :


        If the roots of a polynomial are given,  they  DO  NOT  still define the polynomial in a unique way.

        They determine a polynomial only to the   PROPORTIONALITY  COEFFICIENT  ( ! )