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Mathematics

Solve the following equation by factorisation:

3x2 - 5x - 12 = 0

Quadratic Equations

Answer

Given,

3x25x12=03x29x+4x12=03x(x3)+4(x3)=0(x3)(3x+4)=0 (Factorising left side) x3=0 or 3x+4=0 (Zero-product rule) x=3 or x=433x^2 - 5x - 12 = 0 \\[0.5em] \Rightarrow 3x^2 - 9x + 4x - 12 = 0 \\[0.5em] \Rightarrow 3x(x - 3) + 4(x - 3) = 0 \\[0.5em] \Rightarrow (x - 3)(3x + 4) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x - 3 = 0 \text{ or } 3x + 4 = 0 \text{ (Zero-product rule) }\\[0.5em] \Rightarrow x = 3 \text{ or } x = -\dfrac{4}{3}

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

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