1. Given the quadratic equation (3p+1)x^2 - (p+3)x + 1 =0, find the value(s) of p for each of the following cases.
a) The production of the roots of the equation is -4.
b) The sum of the roots of the equations is 7.
c) The equation has a repeated real root.
2. If A and B are the roots of the quadratic equation x^2 - 3kx +18=0 and A=2B, find the possible value(s) of k.
3. If one root of the quadratic equation -2(x^2) +3(p-1)x-10=0 is less that the other root by 4, find the possible value(s)of p .
4. It is given that A and B are the roots of the quadratic equation x^2 + x = K(2x+3). IF A^2 + B^2 = 43 , find the possible valus(s) of k.
F.4 Maths. Quadratic...
2009-09-26 3:32 am
回答 (2)
2009-09-26 4:52 am
✔ 最佳答案
(1a) Product of roots = 1 / (3p + 1) = -41 = -12p - 4
12p = -5
p = -5/12
(1b) Sum of roots = (p + 3)/(3p + 1) = 7
p + 3 = 21p + 7
20p = -4
p = -1/5
(1c) Repeated roots => Discriminant = 0
(p + 3)^2 - 4(3p + 1) = 0
p^2 + 6p + 9 - 12p - 4 = 0
p^2 - 6p + 5 = 0
(p - 5)(p - 1) = 0
p = 5 or p= 1
(2) Product of roots = 18 = AB
18 = (2B)(B)
B^2 = 9
B = +/-3
when B = 3, A = 6
when B = -3, A = -6
Sum of roots = 3k
when A = 6, B = 3, 3k = 9 => k = 3
when A = -6, B = -3, 3k = -9 => k = -3
(3) Let the roots be a and a - 4
Product of roots = a(a - 4) = (-10)/(-2) = 5
a^2 - 4a - 5 = 0
(a - 5)(a + 1) = 0
a = 5 or a = -1
when a = 5, a - 4 = 1 sum of roots = 6
when a = -1, a - 4 = -5 sum of roots = -6
Sum of roots = -3(p - 1)/(-2) = (3/2)(p - 1)
When sum of roots = 6, (3/2)(p - 1) = 6
p - 1 = 4
p = 5
when sum of roots = -6, (3/2)(p - 1) = -6
p - 1 = -4
p = -3
(4) x^2 + x = k(2x + 3)
x^2 + x - 2kx - 3k = 0
x^2 + (1 - 2k)x - 3k = 0
Sum of roots A + B = 2k - 1
Product of roots AB = -3k
(A + B)^2 - 2AB = (2k - 1)^2 - 2(-3k)
A^2 + B^2 = 4k^2 - 4k + 1 + 6k = 43
4k^2 + 2k - 42 = 0
2k^2 + k - 21 = 0
(2k + 7)(k - 3) = 0
k = -7/2 or k = 3
2009-09-26 4:14 am
1. a) 1/(3p+1)= -4
1= -12p-4
5= -12p
p= 5/-12
b) -(p+3)/(3p+1)=7
-p-3=21p+7
-10=22p
p= -5/11
1= -12p-4
5= -12p
p= 5/-12
b) -(p+3)/(3p+1)=7
-p-3=21p+7
-10=22p
p= -5/11
收錄日期: 2021-04-23 23:18:49
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