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Mathematics

Which of the following quadratic equations has 2 and 3 as its roots?

  1. x2 - 5x + 6 = 0

  2. x2 + 5x + 6 = 0

  3. x2 - 5x - 6 = 0

  4. x2 + 5x - 6 = 0

Quadratic Equations

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Answer

Since, {2, 3} is solution set.

It means 2 and 3 are roots of the equation,

∴ x = 2 or x = 3

⇒ x - 2 = 0 or x - 3 = 0

⇒ (x - 2)(x - 3) = 0

⇒ (x2 - 3x - 2x + 6) = 0

⇒ x2 - 5x + 6 = 0.

Hence, option 1 is the correct option.

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