1. If A nad B are the roots of the equation ax²+bx+c=0, then the roots of the equation 4ax²-2bx+c=0 are ?
Ans+ -A/2, -B/2
2.If the sum of roots of the equation x²+px+p²=0 is 2p-6, the product of roots is?
Ans: 4
*Plz avoid using the A.maths methods as it's maths Qs. THZ!
F.4 maths
2007-10-05 4:22 am
回答 (2)
2007-10-05 4:35 am
✔ 最佳答案
As follows~~~圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/quad2.jpg?t=1191501299
參考: Myself~~~
2007-10-05 4:30 am
A+B = -b/a AB = c/a
For the equation, 4ax²-2bx+c=0
Sum of roots = 2b/4a = b/2a = -(A+B)/2
Product of roots = c/4a = AB/4
Let P and Q be the roots of the equation 4ax²-2bx+c=0
P+Q = -(A+B)/2
PQ = AB/4
P = -Q-(A+B)/2
-Q^2 - (A+B)Q/2 = AB/4
Q^2 + (A+B)Q/2 + AB/4
Q = -B/2 or -A/2 **Using the formula x= [-b+-sqrt(b^2-4ac)]/2**
The answer is -B/2 or -A/2
2.Sum of roots = -p = 2p-6
3p = 6
p = 2
Product of roots = p^2 = 2^2 = 4
Note the sum of roots and products of roots has been out of syllabus in the Maths syllabus.....so these two questions should be A. Maths questions instead.
For the equation, 4ax²-2bx+c=0
Sum of roots = 2b/4a = b/2a = -(A+B)/2
Product of roots = c/4a = AB/4
Let P and Q be the roots of the equation 4ax²-2bx+c=0
P+Q = -(A+B)/2
PQ = AB/4
P = -Q-(A+B)/2
-Q^2 - (A+B)Q/2 = AB/4
Q^2 + (A+B)Q/2 + AB/4
Q = -B/2 or -A/2 **Using the formula x= [-b+-sqrt(b^2-4ac)]/2**
The answer is -B/2 or -A/2
2.Sum of roots = -p = 2p-6
3p = 6
p = 2
Product of roots = p^2 = 2^2 = 4
Note the sum of roots and products of roots has been out of syllabus in the Maths syllabus.....so these two questions should be A. Maths questions instead.
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