Question

If α and β are the roots of the equation (x - a)(x - b) = c, c ≠ 0; then the roots of the equation (x - α)(x - β) +c = 0 are 
1. a and c
2. b and c
3. a and b
4. (a + c) and (b + c)

Answer 1

Correct Answer - Option 3 : a and b

Concept:

Quadratic equations whose roots are α and β is given by 

(x - α)(x - β)

Calculation:

Given that,

(x - a)(x - b) - c     ----(1)

According to the question, α and β are the roots of the equation.

Therefore,

(x - a)(x - b) - c = (x - α)(x - β)

⇒ (x - a)(x - b) = (x - α)(x - β) + c

which represents, root of equation (x - α)(x - β) + c are a and b.