Question

if alpha and beta are the zeros of quadratic polynomial p(x)= x^2-mx+n then find the value of alpha/beta and beta/alpha

Answer 1

Answer: α/β + β/α= m^2/n - 2

Step-by-step explanation:

p(x)= x^2-mx+n

a=1, b= -m, c= n

Sum if zeroes= α+β= -b/a= -(-m)/1= m

So, α+β= m,

Product of zeroes = αβ= c/a= n/1= n,

αβ=n

Now, α^2+β^2= (α+β) ^2 - 2 ×αβ

Divide both sides by αβ,

[α^2+β^2]/αβ= (α+β) ^2/αβ - 2 ×αβ/αβ

α/β + β/α= m^2/n - 2