F4 Math 題目 MC If α and β are the roots of the quadratic equation 2x² -4x-3=0, then 2α² + 4β = ? A)3 B)5 C)9 D)11?

If α and β are the roots of the quadratic equation 2x² - 4x - 3 = 0, then 2α² - 4α - 3 = 0.
2α² = 4α + 3.
Also, sum of roots is α + β = -(-4)/2 = 2.
As a result,
2α² + 4β = 4α + 3 + 4β = 4(α + β) + 3 = 4(2) + 3 = 11.
The answer is D.

2x² -4x-3=0
α+β=2
αβ=-3/2
2α² -4α-3=0
α² + 4β
=(4α+3)+4β
=4(α+β)+3
=4(2)+3
=11(D)

不一定