Question

if alpha and beta are the zeros of the polynomial x2-5x+4 find the value of
1.alpha -beta
2.alpha ^2 +beta^2
3.alpha^4+beta^4
4.alpha beta^2+alpha ^2beta
5.1/alpha +1/beta
6.1/alpha +1/beta-alpha beta
7.1/alpha -1/beta
8.alpha ^3+beta^3
9.alpha/beta+beta/alpha
10.alpha^2/beta+beta^2/alpha
11.alpha/beta+beta/alpha +1/alpha +1/beta+3alpha beta
12.alpha^4 beta^3+alpha^3 beta^4
13.1/alpha +1/beta -2 alpha beta
14.alpha^2/beta^2+alpha^2/beta^2​

Answer 1

Step-by-step explanation:

Consider the given polynomial.

f(x)=x

2

−5x+k

Since, α,β are the zeroes of given polynomial.

So,

α+β=5

αβ=k

Since, α−β=1

Therefore,

2α=1+5

2α=6

α=3

And β=2

Therefore,

3×2=k

k=6