If α, β are roots of the equation x2-2 m x+m2-1=0 then the number of integral value of m for which α, β ∈(-2,4) is :

Question

If α, β are roots of the equation x2-2 m x+m2-1=0 then the number of integral value of m for which α, β ∈(-2,4) is : (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

x=(2 m ± √4 m2-4(m2-1)/2)=(2 m ± 2/2) or m+1 or m-1 Hence -2 < m+1 < 4 ⇒ -3 < m < 3 -2 < m-1 < 4 ⇒ -1 < m < 5 Hence, m ∈(-1,3) ⇒ m=0,1,2

Q. If $α, β$ are roots of the equation $x^{2} - 2 m x + m^{2} - 1 = 0$ then the number of integral value of $m$ for which $α, β \in (- 2, 4)$ is :