Question

If α and β are the zeros of the polynomial f(x) = x² - 5x + k such that α - β = 1, then find k.

Answer 1

So, as the question have given that

$\alpha \: and \: \beta$

are the zeros of the given polynomial

so

$\alpha + \beta = -(\frac{-5}{1}) = 5$

and $\alpha\beta = k$

and, $\alpha - beta = 1$

$(\alpha - \beta)^2 = 1$

$(\alpha + \beta)^2 - 4\alpha\beta = 1$

$25 - 4k = 1 => 24 = 4k$

k = 6

hence value of k is

6