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82Example 9: Find the roots of 4x3x + 5 0 by the method of completing thesquare |
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Answer» 4x² + 3x+ 5= 0First, divide throughout with 4 as the coefficient for x² is 4.→ x2+ 3/4x + 5/4=0now, take 5/4 on the other side....→ x2+ 3/4x = -5/4by using completing square method add the square of the half of the middle term...→x^2+ 3/4x+ (3/8)^2= -5/4 + (3/8)^2we know that, (a + b)2= a^2+ 2ab +b^2. so, by using that........→(x+3/8)^2= -5/4 + 9/64→ (x+3/8)^2 = (-80+9)/64→ (x+3/8)^2= -71/64now, take square root on both sides...→x+3/8 =√-71/8therefore,x=+√-71/8 - 3/8HENCE,x=(+√-71 - 3)/8 OR x= (-√-71-3)/8 |
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