Complex Numbers And Quadratic Equations

Question
CBSEENMA11015662

If (1 – p) is a root of quadratic equation x2 +px + (1-p)=0 , then its roots are

  • 0, 1

  • -1, 2

  • 0, -1

  • -1, 1

Solution

C.

0, -1

Since (1 - p) is the root of quadratic equation
x2 + px + (1 - p) = 0 ........ (i)
So, (1 - p) satisfied the above equation
∴ (1 - p)2 + p(1 - p) + (1 - p) = 0
(1 - p)[1 - p + p + 1] = 0 (1 - p)(2) = 0
⇒ p = 1 On putting this value of p in equation (i)
x2 + x = 0
⇒ x(x + 1) = 0 ⇒ x = 0, -1

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