a*****g
发帖数: 1320 | 1 1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x+3=
0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
Express your answer as a common fraction
4) What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
5) The solutions of X3-63x2+cx-1728=0 form a geometric sequence. What is the
value of c?
Thanks a lot! | r****c
发帖数: 2585 | 2 1) first one
assume solution of x^2 + 7x + 3 = 0 is x_1, x_2,
then
(x - x_1)(x-x_2) = x^2 + 7x + 3
which gives u
x_1 + x_2 = -7
x_1 * x_2 = 3
so (x-x_1-5)(x-x_2-5)= x^2 + bx + c
which gives you b = -(x_1+x_2+10) = -(-7 + 10) = -3
c = (x_1 + 5) * (x_2 + 5) = x_1 * x2 + (x_1+x_2) * 5 + 25 = 3 + 5 *(-7) + 25
= -7
use the same trick for following ones | s****t
发帖数: 461 | 3
3=
b,
(-3, -7)
x
(-12, 47, -60)
13/15
93
the
756
【在 a*****g 的大作中提到】
: 1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x+3=
: 0. What are the value of b and c? Express your answer as an ordered pair (b,
: c)
: 2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
: =5. What are the value of b, c, and d? Express your answer as an ordered
: triple (b,c,d)
: 3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
: Express your answer as a common fraction
: 4) What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
: 5) The solutions of X3-63x2+cx-1728=0 form a geometric sequence. What is the
| a*****g
发帖数: 1320 | 4 Super many thanks you guys great help!! |
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