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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

Given,

2x2−9x+10=0⇒2x2−5x−4x+10=0⇒x(2x−5)−2(2x−5)=0⇒(x−2)(2x−5)=0 (Factorising left side) ⇒x−2=0 or 2x−5=0 (Zero-product rule) ⇒x=2 or x=522x^2 - 9x + 10 = 0 \\[0.5em] \Rightarrow 2x^2 - 5x - 4x + 10 = 0 \\[0.5em] \Rightarrow x(2x - 5) - 2(2x - 5) = 0 \\[0.5em] \Rightarrow (x - 2)(2x - 5) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x - 2 = 0 \text{ or } 2x - 5 = 0 \text{ (Zero-product rule) } \\[0.5em] \Rightarrow x = 2 \text{ or } x =\dfrac{5}{2}

(i) Hence, the root of given equation is 2 , when x ∈ N

(ii) Hence, the root of given equation is 2, 52\dfrac{5}{2} , when x ∈ Q

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