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Determine whether the given quadratic equation has real roots or not. x 2- 2x + 1 = 0. |
| Answer» We have been given,\xa0x2\xa0- 2x\xa0+ 1 = 0Now we also know that for an equation ax2\xa0+ bx + c = 0, the discriminant is given by the following equation:D = b2\xa0- 4acNow, according to the equation given to us, we have,a = 1, b = -2 and c = 1.Therefore, the discriminant is given as,D = (-2)2\xa0- 4(1)(1)= 4 - 4= 0Since, in order for a quadratic equation to have real roots, D\xa0≥ 0.Here we find that the equation satisfies this condition, hence it has real and equal roots.Now, the roots of an equation is given by the following equation,x=-b± underroot D / 2aTherefore, the roots of the equation are given as follows,x=-(-2)±0 / 2(1)=2 / 2= 1Therefore, the roots of the equation are real and equal and its value is 1. | |