If α and β are the zeroes of the polynomial $$x^2-5x+m$$​ such that α – β = 1, then what will be the value of $$m$$​.

Correct option is C

Given:

The polynomial is x$$^2$$​ - 5x + m, and the roots α and β satisfy α – β = 1

Concept Used:
$$\alpha + \beta = -\frac{b}{a} \quad \text{and} \quad \alpha \beta = \frac{c}{a}$$​

Solution:
$$\alpha + \beta = -\frac{-5}{1} = 5 \quad \text{and} \quad \alpha \beta = \frac{m}{1}$$​ = m

​$$\alpha + \beta = 5 \quad \text{and} \quad \alpha \beta$$​ = m

$$\alpha$$​ – β = 1

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

1$$^2 = 5^2$$​ - 4m

1 = 25 − 4m

4m = 25 - 1

4m = 24

m = 6