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Mathematics

Solve the following equation by factorisation:

2x2 - 9x + 10 = 0, when :

(i) x ∈ N

(ii) x ∈ Q.

Quadratic Equations

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Answer

2x2 - 9x + 10 = 0

⇒ 2x2 - 4x - 5x + 10 = 0

⇒ 2x(x - 2) - 5(x - 2) = 0

⇒ (2x - 5)(x - 2) = 0

⇒ 2x - 5 = 0 or x - 2 = 0      [Using Zero-product rule]

⇒ 2x = 5 or x = 2

⇒ x = 52\dfrac{5}{2} or x = 2.

(i) Since, x ∈ N

Hence, value of x = 2.

(ii) Since, x ∈ Q

Hence, value of x = 52\dfrac{5}{2} or 2.

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