Quadratic EquationEasy
Question
If (1 - p) is a root of quadratic equation x2 + px + (1 - p) = 0, then its roots are
Options
A.0, 1
B.-1, 2
C.0, -1
D.-1, 1
Solution
(1 - p)2 + p(1 - p) + (1 - p) = 0 (since (1 - p) is a root of the equation x2 + px + (1 - p) = 0)
⇒ (1 - p)(1 - p + p + 1) = 0
⇒ 2(1 - p) = 0 ⇒ (1 - p) = 0 ⇒ p = 1
sum of root is α + β = - p and product αβ = 1 - p = 0 (where β = 1 - p = 0)
⇒ α + 0 = - 1 ⇒ α = - 1 ⇒ Roots are 0, - 1
⇒ (1 - p)(1 - p + p + 1) = 0
⇒ 2(1 - p) = 0 ⇒ (1 - p) = 0 ⇒ p = 1
sum of root is α + β = - p and product αβ = 1 - p = 0 (where β = 1 - p = 0)
⇒ α + 0 = - 1 ⇒ α = - 1 ⇒ Roots are 0, - 1
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