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John and Jane started

by sanju09 » Thu Aug 12, 2010 3:22 am
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


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by kvcpk » Thu Aug 12, 2010 3:44 am
sanju09 wrote: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


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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.
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