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

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