Question

If α, β are the zeroes of the polynomial f(x) = x² – 5x + k such that α – β = 1, find the value of k = ?

If α and β are the zeroes of the polynomial f(x) = x² – 5x + k such that α – β = 1, find the value of k.

Answer 1

By using the relationship between the zeroes of the quadratic polynomial.

We have  

Sum of zeroes = `(-("Coefficient of"  x))/("Coefficient of"  x^2)` and Product of zeroes = `("Constant term")/("Coefficient of "x^2)`   

∴ `α + β = (-(-5))/1` and `αβ = k/1`

⇒ α + β = 5 and αβ = `k/1`

Solving α – β = 1 and α + β = 5, we will get 

α = 3 and β = 2 

Substituting these values in αβ = `k/1`, we will get 

k = 6