If 3 is one root of the quadratic equation 2x^2 - 5x + k = 2, where k

Question

If 3 is one root of the quadratic equation  2x^2 - 5x + k = 2 , where k is a constant, what is the equation’s other root?

(A) -3
(B) -1/2
(C) -1
(D) 1/2
(E) 3

GMATinsight · Answer

If 3 is one of the roots then it must satisfy the equation  2x^2 - 5x + k = 2

i.e.  2(3)^2 - 5(3) + k = 2

i.e.  18 - 15 +k = 2

i.e.  k = -1

Now the equation becomes  2x^2 - 5x -3 = 0

Now we have three option

1) Either substitute options and whichever option satisfies the equation will be the correct answer

2) Sum of the roots =  -b/a  in a quadratic equation  ax^2 - bx + c = 0

i.e. sum of the roots of  2x^2 - 5x -3 = 0  is given by
Sum = - (-5)/2 = 5/2

i.e. 3 + p = 5/2 . { If p is the second root and we know that 3 is the first root }

i.e. p = -1/2

3) Factorise the equation
 2x^2 - 5x - 1 = 2 .
  2x^2 - 5x - 3 = 0 .
  2x^2 - 6x + x - 3 = 0 .
2x(x-3) +1(x-3) = 0
(2x+1) (x-3) = 0.
x = -1/2 and x =3 are the two roots.

One of the roots is given as 3, the other root is x=-1/2

Answer: Option B

LevanKhukhunashvili · Answer

GMATinsight

Why if k=-1
You get 2x^2-5x-1= 0  and not 2x^2-5x-1= 2

Got lil confused

Bunuel · Answer

You are right. There is a small typo in that solution. We got that k = -1, so the equation is  2x^2 - 5x - 1= 2  -->  2x^2 - 5x - 3= 0  --> x = 3 or x = -1/2.

Answer: B.

SSM700plus · Answer

2x^2 - 5x + k = 2 . One of the root is 3.

Substitute x=3 in the equation.

2(3)^2 - 5(3) + k = 2 .
2*9 - 15 +k = 2.
k+3=2
k= -1.

use k=-1 to get the general equation without constant k.
  2x^2 - 5x - 1 = 2 .
  2x^2 - 5x - 3 = 0 .
  2x^2 - 6x + x - 3 = 0 .
2x(x-3) +1(x-3) = 0
(2x+1) (x-3) = 0.
x = -1/2 and x =3 are the two roots.

3 is given root. x=-1/2 is the 2nd root.

Ans - B.

thefibonacci · Answer

sum of roots = -b/a 
3+p = 5/2
p = -1/2

rahul16singh28 · Answer

Here, we dont need to find the value of K.

Sum of roots = 5/2
3 + x = 5/2 ---> x = -1/2

ColumbiaEMBA · Answer

Plug in 3 for X and solve for K. K = -1. Now plug in answer choices starting from A. B is the only one which results in 2 which is what the original equation equals.

JeffTargetTestPrep · Answer

We can create the equation:

2(3^2) - 5(3) + k = 2

18 - 15 + k = 2

k = -1

So we now have:

2x^2 - 5x - 1 = 2

2x^2 - 5x - 3 = 0

(2x + 1)(x - 3) = 0

2x + 1 = 0

x = -1/2

Answer: B

u1983 · Answer

Given equation :  2x^2 - 5x + k = 2 
 or  x^2 - \frac{5}{2}x + \frac{k}{2} = 1 
 or  x^2 - \frac{5}{2}x + ( \frac{k}{2} -1)= 0  is equivalent to the std quadratic expression  x^2 - (b+c)x + bc= 0  where b and c are two roots of the equation.

now we have 1 root as 3 , lets assume the other root is c

Hence ,  - \frac{5}{2} = - (3+c) 
 or  \frac{5}{2} = (3+c) 
 or  c = \frac{5}{2} - 3 
Hence  c= -\frac{1}{2} ..........................Hence I would go for  option B.

manishGg30 · Answer

We can solve it by using the product of roots and sum of roots (NO NEED TO CALCULATE K)

Let m and n be the roots of the equation

sum of roots = -b/a (i.e m+n = 5/2)

we know that 3 is one of the root of the equation so,

n comes out to be (-1/2)

bumpbot · Answer

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If 3 is one root of the quadratic equation 2x^2 - 5x + k = 2, where k

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