Question

Find the values of m for which exactly one root of the equation x^2-2mx+m^2-1 lies in the interval (-2 , 4) then m belongs to

Answer 1

sol is attached. value of multiplication at -2 & 4 should be negative

Answer 2

Answer:

root of the equation - x^2-2mx+m^2-1

m lies in the interval (-2,4)

substitute the value of x

(-2)^2-2m(-2)+m^2-1

4+4m+m^2-1

4^2-2m(2)+ m^2-1

16-8m+m^2-1

(4+4m+m^2-1)(16-4m+m^2-1)

(m^2+8m+15)(m^2-4m+3)

(m-5)(m-3)(m+1)(m+3)

m€(-3,-5) U m€(3,5)