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一元二次方程ax2+bx+c=0(a≠0)的系数和a+b+c=0,则x=1满足方程ax2+bx+c=0,即x=1是该方程的一个根.反过来,x=1是一元二次方程ax2+bx+c=0(a≠0)的一个根,则a+b+c=0.运用这个结论可解决不少的问题.请看:例1解方程:4x2-5x+1=0.分析与解:因为4+(-5)+1=0,所以x1=1是方程的一个根.设另一根为x2,由根与系数的关系,得1×x2=14,即x2=14,所以方程的解是x1=1,x2=14.
When the coefficient of a quadratic equation ax2 + bx + c = 0 (a ≠ 0) and a + b + c = 0, then x = 1 satisfies the equation ax2 + bx + c = 0, ie x = 1 is one of the equations In turn, x = 1 is a root of the quadratic equation ax2 + bx + c = 0 (a ≠ 0), then a + b + c = 0. Applying this conclusion can solve quite a few problems. : Example 1 Solve the equation: 4x2-5x + 1 = 0. Analyze the solution: Since 4 + (- 5) + 1 = 0, so x1 = 1 is a root of the equation. The relationship between the coefficients, 1 × x2 = 14, that is, x2 = 14, so the solution of the equation is x1 = 1, x2 = 14.