John and Jane started

[sanju09]

John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4. What is the equation?
(A) x^2 + 4 x + 14 = 0
(B) 2 x^2 + 7 x - 24 = 0
(C) x^2 - 14 x + 48 = 0
(D) 3 x^2 - 17 x + 52 = 0
(E) 2 x^2 + 4 x +14 = 0


[spoiler]Source: freegmattest.net[/spoiler]

[kvcpk]

John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4. What is the equation?
(A) x^2 + 4 x + 14 = 0
(B) 2 x^2 + 7 x - 24 = 0
(C) x^2 - 14 x + 48 = 0
(D) 3 x^2 - 17 x + 52 = 0
(E) 2 x^2 + 4 x +14 = 0


[spoiler]Source: freegmattest.net[/spoiler]

ax^2 +bx+c
sum of roots = -b/a
product of roots = c/a

in John's case sum of roots should be correct.
x+y = 14 = -b/a
In Jane's case prodcut is correct.
xy = 48 = c/a

From among the options, only C satisfies this.