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Mathematics

Solve the following equation by factorisation:

x2 - 3x - 10 = 0

Quadratic Equations

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Answer

Given,

x23x10=0x25x+2x10=0x(x5)+2(x5)=0(x+2)(x5)=0 (Factorising left side) x+2=0 or x5=0 ( Zero - product rule) x=2 or x=5x^2 - 3x - 10 = 0 \\[0.5em] \Rightarrow x^2 - 5x + 2x - 10 = 0 \\[0.5em] \Rightarrow x(x - 5) + 2(x - 5) = 0 \\[0.5em] \Rightarrow (x + 2)(x - 5) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x + 2 = 0 \text{ or } x - 5 = 0 \text{ ( Zero - product rule) }\\[0.5em] \Rightarrow x = -2 \text{ or } x = 5

Hence, the roots of given equation are -2, 5.

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