Question

let P(x)=x2-(2-P)x+P-2 If P(x)assumes both positive and negative values for x belongs to real numbers then the range of P is:
PLS HELP URGENT WILL MARK BRAINLIEST
also the options are -infinity,2 union 6,infinity
2,6
-infinity,2
6,infinity

Answer 1

Answer:

First suppose that the roots of the equation

x2−bx+c=0(1)

are real and positive. From the quadratic formula, we see that the roots of (1) are of the form

b±b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√2.

For the root or roots to be real, we require that b2−4c≥0, that is, b2≥4c. In order for them to be positive, we require that

b−b2−4c⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√>0.