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how do you write a quadratic function with zeros 3/7 and -4?

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2 Answers

  Postulate :Every quadratic of aX2 + bX + c   has roots of m, n if and only if
                                              aX2 +bX +c  can be  factored into  ( x -m ) ( X -n)
  accordingly :
f(x) = ( X +4) ( X -3/7) = X2 + 4X -3/7X - 12/7
                                       7X2 +28X - 3X - 12=
                                        7X2 + 25X - 12
if they give you the zeroes (also called roots) you can get the function ax^2+bx+c
by using the product of the roots and the sum of the roots
the sum of the roots will come out to be -b/a
the product of the roots is c/a
so the sum of your roots in your case (3/7 - 4) would be -25/7
the product of your roots 3/7 * -4 would be -12/7
so we have sum of roots -25/7 = -b/a
                 product of roots -12/7 = c/a
you can match up the a, b and c
a=7  b=25 (watch your signs) and c=-12