If the two roots of a quadratic equation are α, β where α + β = 8 and α - β = 2, then the equations:

Sum of roots α + β = 8

Difference of roots α – β = 2

In a quadratic equation of the form $$x^2 - ( \alpha + \beta )x + \alpha \beta = 0:$$​​

The sum of the roots α + β is the coefficient of x (with opposite sign).

The product of the roots αβ is the constant term.

α + β = 8………(1)
α - β = 2 ………(2)
from equation (1) and (2)
α = 5, β =3
as we know
quadratic equation which two roots are given is
​$$x^2 – x \text{(sum of roots)} + \text{(product of roots)}=0\\\text {after putting the value of α and β}\\x^2 – 8x +15 =0\\$$​​​