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If (1-p) is a root of quadratic equation...

If `(1-p)` is a root of quadratic equation `x^2+p x+(1-p)=0,` then find its roots.

Text Solution

Verified by Experts

The correct Answer is:
`x = 0, -1`
Since ( 1 - p) is the root of quadration equation
`x^(2) + px + (1 - p) = 0`
So (1 - p) satisfies the above equation. Therefor,
`(1 - p)^(2) + p (1 - p) + (1 - p) = 0`
or `( 1 - p)[1 - p + p + 1] = 0`
or `(1-p) (2) = 0`
or ` p = 1`
On putting this value of p in Eq. (1), we get
`x^(2) + x = 0`
or ` x(x + 1) = 0`
or `x = 0, -1`
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