Question

Questions) If both roots of quadratic equation (2-x)(x+1)=p are distinct and positive , then find interval in which P lie

Answer 1

(2-x)(x+1)=p
2x + 2 - x^2 - x = p
-x^2 -x +2 = p
x^2-x +p-2 = 0
Simce, the equation has two distinct roots, hence its D > 0
b^2 -4ac > 0
1^2 -4.1.(p-2) >0
1-4p+ 8 >0
-4p+9>0
-4p > -9
4p< 9
p< 9/4
p ∈( -∞,9/4)