One of the two students while solving a quadratic equation in \(x\) copied the constant term incorrectly and got his roo

[Gmat_mission]

One of the two students while solving a quadratic equation in \(x\) copied the constant term incorrectly and got his roots as \(3, 2.\) The other copied the constant and coefficient term of \(x^2\) correctly as \(-6, 1\) respectively. The correct roots of the equation are?

(A) \(3, -2\)
(B) \(-3,2\)
(C) \(3,3\)
(D) \(-6,-1\)
(E) \(6,-1\)

Answer: E

Source: e-GMAT

[Scott@TargetTestPrep]

One of the two students while solving a quadratic equation in \(x\) copied the constant term incorrectly and got his roots as \(3, 2.\) The other copied the constant and coefficient term of \(x^2\) correctly as \(-6, 1\) respectively. The correct roots of the equation are?

(A) \(3, -2\)
(B) \(-3,2\)
(C) \(3,3\)
(D) \(-6,-1\)
(E) \(6,-1\)

Answer: E

Solution:

Since the incorrect roots are 3 and 2, the incorrect quadratic equation is:

(x - 3)(x - 2) = 0

x^2 - 5x + 6 = 0

Since the only term that is wrong is the constant term (6) and since the correct constant term is -6, the correct quadratic equation is x^2 - 5x - 6 = 0. Solving this equation by factoring, we have:

(x - 6)(x + 1) = 0

x = 6 or x = -1

Answer: E