Mathematics

If x2 + kx + 6 = (x - 2)(x - 3) for all values of x, then the value of k is :

  1. -5

  2. -3

  3. -2

  4. 5

Quadratic Equations

ICSE Sp 2024

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Answer

Given,

⇒ x2 + kx + 6 = (x - 2)(x - 3)

⇒ x2 + kx + 6 = x2 - 3x - 2x + 6

⇒ x2 + kx + 6 = x2 - 5x + 6

⇒ x2 - x2 + kx + 6 - 6 = -5x

⇒ kx = -5x

⇒ k = -5.

Hence, Option 1 is the correct option.

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