The expression ( x 2+2 x +1/ x 2+2 x +7) lies in the interval ; ( x ∈ R ) -

Question

The expression ( x 2+2 x +1/ x 2+2 x +7) lies in the interval ; ( x ∈ R ) - (A) [0,-1] (B) (-∞, 0] ∪[1, ∞) (C) [0,1) (D) none of these

Tardigrade Admin · Accepted Answer

(x2+2 x+1/x2+2 x+7)=y ⇒ x2(1-y)+x(2-2 y)+1-7 y=0 D>0 ⇒ 6 y(y-1)<0 ⇒ y ∈[0,1)

Q. The expression $\frac{x ^{2} + 2 x + 1}{x ^{2} + 2 x + 7}$ lies in the interval ; $(x \in R)$ -