Give that a and b are integers,where a≠0.prove that the quadratic equation
ax^2 +4bx -(a-4b)=0has rational roots
maths question
2007-10-13 8:20 pm
回答 (1)
2007-10-13 8:26 pm
✔ 最佳答案
Discriminant (D) = (4b)^2 -4(a)(-a+4b)D=16b^2 +4a^2 -16ab
D=4(a^2-4ab+4b^2)
D=4(a-2b)^2
Since the two roots are (-4b+sqrt(D))/2a or (-4b-sqrt(D))/2a, and a and b are integers.
sqrt(D) must be integer. As a result, the two roots must be rational
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