given that A and B are the roots of the quadrtic equation
ax^2 +bx +c=0
where a≠0.find the quadratic equation in x with roots A+2B and B+2A.
maths question
2007-10-13 8:22 pm
回答 (1)
2007-10-13 8:29 pm
✔ 最佳答案
A+B = -b/a and AB = c/aSum of required roots = A+2B+B+2A = 3A+3B = -3b/a
Product of required roots = (A+2B)(B+2A) = 2A^2+2B^2 +5AB
= 2(A^2+2AB+B^2)+AB = 2(A+B)^2+AB
=2(b^2/a^2) + c/a
=(2b^2+ac)/a^2
Required equation is x^2 +(3b/a)x +(2b^2+ac)/a^2 = 0
i.e a^2x^2 +3abx +2b^2+ac = 0
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