If a and b are non-zero distinct real numbers, determine the nature of the roots of the following quadratic equations.
1. x^2+(b-a)x+(a-b)^2=0
2. -2(a+1)x^2+(a-4)x+3a-2=0 for a is not = -1
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maths question
2009-08-20 6:11 am
回答 (2)
2009-08-20 7:24 am
✔ 最佳答案
1. △=(b-a)2-4(1)(a-b)2
=(b-a)2-4(b-a)2
=-3(b-a)2
<0
The equation has no real root.
2.△=(a-4)2-4[-2(a+1)](3a-2)
=(a2-8a+16)+8(a+1)(3a-2)
=a2-8a+16+8(3a2+a-2)
=a2-8a+16+24a2+8a-16
=25a2
>0
The equation has two distinct real roots.
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