quadratic equation

1.
x + 1/x = 29/10
10x² + 10 = 29x (Multiplying 10x on both sides)
10x² - 29x + 10 = 0
(5x - 2)(2x - 5) = 0
x = 2/5 or x = 5/2

2.
Product of roots = 5/4
So c(c+2) = 5/4
4c(c+2) = 5
4c² + 8c - 5 = 0
(2c + 5)(2c - 1) = 0
c = -5/2 or c = 1/2

If c = -5/2, c+2 = -1/2.
So -p/4 = Sum of roots = -5/2-1/2 = -3. Therefore p = 12

If c = 1/2, c+2 = 5/2
So -p/4 = Sum of roots = 1/2+5/2 = 3. Therefore p = -12.

(1)
x+(1/x)=29/10
(x^2+1)/x=29/10
x^2-29x/10+1=0
10x^2-29+10=0
x=[29士1241sqrt.]/20
Which sqrt. means square root.]

(2)
-p/4=c+c+2......(1)
5/4=c(c+2).......(2)

(1):c=-(p+8)/8......(3)
c^2+2c=5/4......(4)
Sub (3) into (4)
[-(p+8)/8]^2-(p+8)/8=5/4
(p^2+16p+64)/64-8(p+8)/64=5/4
p^2+16p+64-8(p+8)=80
p^2+16p+64-8p-64=80
p^2+8p-80=0
p=-4士96sqrt.

1) x+1/x = 29/10
(x^2+1)/x = 29/10
10(x^2+1)=29x
10x^2+10-29x=0
10x^2-29x+10=0
(5x-2)(2x-5)=0
x=2/5 or x=5/2


2) Product of roots = c(c+2)=5/4 ==>c^2+2c=5/4==>4c^2+8c=5==>4c^2+8c-5=0
==>(2c-1)(2c+5)=0==>c=1/2 or c=-5/2

Sum of roots = c+(c+2)=-p/4 ==>p=-4(2c+2)

So, when c=1/2, p = -4(2(1/2)+2)=-12 and when c=-5/2, p=-4(2(-5/2)+2)=12