Solving Quadratic equation by method of Completion of Square
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 Solving Quadratic equation by method of Completion of Square Example : Solve the quadratic equation x2 - 7x - 5 = 0. Solution : Comparing the given equation with ax2+ bx + c = 0, we find that a=l,6 = -7 and c = -5. Therefore, D = (-7)2 - 4 * 1 * (- 5) = 49 + 20 = 69 > 0 Since D is positive, the equation has two roots given by (7 + 69)/6, (7 - 69)/6 i.e. x = (7 + 69)/6, (7 - 69)/6 are the required solutions. Example : Determine value (s) of p for which the quadratic equation 2x2 + px + 8 = 0 has real roots. Solution : D = b2- 4ac b2- 4 * 2 * 8 For the equation having real roots, D > 0, i.e., p2-64>0 or p2 >64, i.e., p2 >82 This gives p>8 or p<-8. [Note: p2-82 >0gives (p + 8)(p - 8)>=0 (1) (1) holds if (i) p + 8 > 0 and p - 8 > 0 i.e., p>-8 and p>8 These give p > 8. or (ii) p + 8 < 0 and p - 8 < 0 i.e., p<-8 and p<8 These give p < -8. Therefore, required values of p are p > 8 or p <-8
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