Let α and β be the roots of the equation x² - ax - bx + ab - c = 0. What is the quadratic equation whose roots are a and b?

Formula used:

If α and β are the roots of quadratic equation ax2 + bx + c = 0

Sum of the roots: α + β = -b/a

Product of the roots: αβ = c/a

Quadratic equation with roots α and β can be written as

x² - (α + β)x + αβ = 0

Calculation: 

Given that α and β be the roots of the equation

x2 - ax - bx + ab - c = 0   

⇒ x² - (a + b)x + (ab - c) = 0 

Hence, sum of the roots 

α + β  = a + b        -----(1)

Product of the roots

αβ = ab - c

⇒ ab = αβ + c      -----(2)

Hence, quadratic equation with roots a & b is 

x2 - (a + b)x + ab = 0      

Put the value from the equations (1) & (2).

⇒ x² - (α + β)x + αβ + c = 0

∴ x² - αx - βx + α β + c = 0