If one root of th

Given: quadratic equation 2x²+kx-6=0

One root = 2

To find: The value of another root.

Formula used: If “p” is root of quadratic equation ax²+bx+c=0

Then a(p)²+b(p)+c=0

Explanation:

Since x=2 is the root of the equation 2x²+kx-6=0,

⇒ 2(2)²+k (2)-6=0

⇒ 2(4) +2k-6=0

⇒ 8 +2k-6=0

⇒ 2+2k=0

⇒ 2 = -2k

⇒ k = -1

Now put the value of k in the equation to get,

2x²+(-1) x-6=0

⇒ 2x²-x-6=0

⇒ 2x²-4x+3x-6=0

⇒ 2x(x-2) +3(x-2) =0

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

x = -3/2 or x = 2

Therefore, the other root is -3/2.