數學問題S4 MC題關於quadratic equatio

If α and β are the roots of the equation x^2 - 3x + k = 0, that means

α^2 - 3α + k = 0 and β^2 - 3β + k = 0.

Therefore, 3α = α^2 + k by the first equation.

Now, 3α + β^2 = α^2 + k + β^2
　　　　　　 = α^2 + β^2 + k
　　　　　　 = α^2 + 2αβ + β^2 + k - 2αβ
　　　　　　 = (α + β)^2 + k - 2αβ
　　　　　　 = (3)^2 + k - 2(k)
　　　　　　 = 9 - k

Thus, the correct answer is C.

2013-08-09 16:14:10 補充：
螞蟻雄兵 的答案較佳，因為牽涉的項目少一點，而且degree亦低一點（由二次變成一次）。

請學習。　：）

Let k be constant.If α and β are the roots of the equation x^2－3x+k=0，then 3α+β^2?
Sol
x^2－3x+k=0
x^2=3x－k
β^2=3β－k
3α+β^2
=3α+3β－k
=3*3－k
=9－k