We have given a quadratic polynomial f(x)=x²-5x+k and α and β are the zeroes of the given polynomial and it is also given that α-β=1 and we have to find the value of k.
This is the important and conceptual question from polynomials as it was already asked in previous year papers
Please give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2C, question no 21
Given : α and β zeroes of f(x)=x²−5x+k and α−β=1
we know that ,
α+β = sum of zeros = -(coefficient of x)/(coefficient of x²) =5
αβ = product of zeroes =(constant term)/(coefficient of x²) =k
Now, solving α−β=1 and α+β=5 we get
α=3 and β=2
Now, αβ=k (putting value of α and β)
k=6