Q) If one root of the quadratic equation $\mathrm{2X}{2}^{}+\mathrm{kX}-6=0$ is 2, find the value of k. Also, find the other root.

Ans: We know that a root of a polynomial satisfies the polynomial.

Here, we are given that X = 2 is the root of the equation 2X² + kX – 6 = 0

∴  2 (2)² + k (2) – 6 = 0

∴  8  + 2 k – 6 = 0

∴   k = – 1

Next, to find the roots, we should make the quadratic equation and then solve it. Let’s start with transferring k = −1 in the equation 2X² + kX − 6 = 0, we get:

2X² + ( -1) X − 6 = 0

∴ 2X² – X − 6 = 0

∴ 2 X² – 4 X + 3 X − 6 = 0

∴ 2 X (X – 2) + 3 (X – 2) = 0

∴ (X – 2) (2X + 3) = 0

∴  X  = 2, X  =

Therefore, other root is .

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