Help with roots and coefficients of polynomials (1 Viewer)

[Green Pup]

I've run into some problems with these:

1)Find values of k if
x^2-(k+2)x+k+1=0
(A) has consecutive roots
(B) reciprocal roots

2)If x=2 is double root of ax^4-2x^3-8x+16=0, find the value of a and the sum of the other two roots

 

[braintic]

1. (A) Let the roots be a and a+1.

a+(a+1)=k+2
2a=k+1

a(a+1)=k+1=2a (from previous)
a^2-a=0
a=0,1
k=-1,1

(B) Let roots be a, 1/a
Product: 1=k+1
k=0

2. Sub in: 16a-16-16+16=0
a=1


Let roots be 2, 2, p, q

Sum: 4+p+q=2
p+q=-2

 

[Green Pup]

Derp. Made some ridiculous mistakes in my working.
Thanks braintic

 

[braintic]

As I'm in my 40s, I don't know 'Derp'. Can I assume it is the same as 'Doh' ?

 

[RealiseNothing]

As I'm in my 40s, I don't know 'Derp'. Can I assume it is the same as 'Doh' ?

It pretty much means "wow I'm an idiot".

 

[Green Pup]

Yep^
Edit:
Actually there's another two more:
Two roots of x^3+mx^2+15x-7=0 are equal and rational. Find m.

Solve 6x^4+5x^3-24x^2-15x+18=0