If one root of 2x2+kx-6=0 is 2. find the value of k and the other root.
The given quadratic equation is
2x2+ kx- 6 = 0
putx= 2 in the above equation, we get
2(2)2+k(2) - 6 = 0
so, 8 + 2k - 6 = 0
⇒ 2k + 2 = 0
⇒ 2k = -2
⇒k = -1
so the equation becomes,
2x2-x- 6 = 0
⇒ 2x2- 4x+ 3x- 6 = 0
⇒ 2x(x- 2) + 3(x- 2) = 0
⇒ (2x+ 3) (x- 2) = 0
⇒ 2x+ 3 = 0 orx- 2 = 0
⇒x= -3/2 orx= 2
so the other root is-3/2