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Mathematics

Solve the following equation by factorisation:

x2 - (p + q)x + pq = 0

Quadratic Equations

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Answer

Given,

x2(p+q)x+pq=0x2pxqx+pq=0x(xp)q(xp)=0(xq)(xp)=0 (Factorising left side) xq=0 or xp=0 (Zero-product rule)x=q or x=p.x^2 - (p + q)x + pq = 0\\[0.5em] \Rightarrow x^2 - px - qx + pq = 0 \\[0.5em] \Rightarrow x(x - p) - q(x - p) = 0 \\[0.5em] \Rightarrow (x - q)(x - p) = 0 \text{ (Factorising left side) }\\[0.5em] \Rightarrow x -q = 0 \text{ or } x - p = 0 \text{ (Zero-product rule)}\\[0.5em] \Rightarrow x = q \text{ or } x = p. \\[0.5em]

Hence, the roots of given equation are p, q.

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