✔ 最佳答案
1) Think about 2 nos., sum of them is 11, product of them is -14.
Let the 2 nos be (a + √b), (a - √b)
It is easy to find that a is 5.5, and
a^2 - b = -14
ie. b = 16.25
So the 2 nos. are (5.5 + √16.25) and (5.5 - √16.25). That is,
x^2 + 11x - 14 = 0
(x + 5.5 + √16.25)(x + 5.5 - √16.25) = 0
x = (-5.5 - √16.25) or (-5.5 + √16.25)
2) Change the equation to
x^2 + 0.4x + 0.6 = 0
Same as Q1, it is easy to find that a is 0.2, and
a^2 - b = 0.6
ie. b = -0.56
As b is negative, the 2 nos. are complex numbers. That is no real roots or
5x^2 + 2x + 3 = 0
x^2 + 0.2x + 0.6 = 0
(x + 0.2 + i√0.56)(x + 0.2 - i√0.56) = 0
x = (-0.2 - i√0.56) or (0.2 + i√0.56)