Quadratic EquationHard
Question
Let α, β be the roots of the equation (x - a)(x - b) = c, c ≠ 0
Then the roots of the equation (x - α)(x - β) + c = 0
Then the roots of the equation (x - α)(x - β) + c = 0
Options
A.a, c
B.b, c
C.a, b
D.a + c, b + c
Solution
Given α, β are the roots of (x - a)(x - b) - c = 0
⇒ (x - a)(x - b)- c = (x - α) (x - β)
⇒ (x - a)(x - b) = (x - α)(x - β) + c
⇒ a, b are the roots of equation (x - α)(x - β) + c = 0
⇒ (x - a)(x - b)- c = (x - α) (x - β)
⇒ (x - a)(x - b) = (x - α)(x - β) + c
⇒ a, b are the roots of equation (x - α)(x - β) + c = 0
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