A]write down all positive integers a such that a+3b=7 , where b is a positive integer.
B]write down all values of k such that 3x^2 +7x+k=(3x+a)(x+b), where a and b are positive integers
f.4 mathz.
2010-07-09 12:01 am
回答 (1)
2010-07-09 12:16 am
✔ 最佳答案
A]a+3b = 7
when b = 1 , a = 4 ;
when b = 2 , a = 1 ;
when b>= 3 , a is not positive.
B]
3x^2 +7x+k=(3x+a)(x+b)
3x^2 + 7x + k = 3x^2 + (a+3b)x + ab
compare with the x term and the constant term ,
a + 3b = 7
and
ab = k
by A] ,
a = 1 , b = 2 , so k = ab = 1*2 = 2
or
a = 4 , b = 1 , so k = ab = 4*1 = 4
k = 2 or 4
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