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Mathematics

Solve the following equation by factorisation:

3x2 = x + 4

Quadratic Equations

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Answer

Given,

3x2=x+4⇒3x2−x−4=0 (Writing as ax2+bx+c=0)⇒3x2−4x+3x−4=0⇒x(3x−4)+1(3x−4)=0⇒(x+1)(3x−4)=0 (Factorising left side) ⇒x+1=0 or 3x−4=0 (Zero-product rule) ⇒x=−1 or x=433x^2 = x + 4 \\[0.5em] \Rightarrow 3x^2 - x - 4 = 0 \text{ (Writing as } ax^2 + bx + c = 0)\\[0.5em] \Rightarrow 3x^2 - 4x + 3x - 4 = 0 \\[0.5em] \Rightarrow x(3x - 4) + 1(3x - 4) = 0 \\[0.5em] \Rightarrow (x + 1)(3x - 4) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x + 1 = 0 \text{ or } 3x - 4 = 0 \text{ (Zero-product rule) }\\[0.5em] \Rightarrow x = -1 \text{ or } x = \dfrac{4}{3}

Hence, the roots of given equation are -1, 43\dfrac{4}{3}.

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