If x is complex, the expression (x2+34 x-71/x2+2 x-7) takes all values which lie in the interval (a, b), find the values of a and b

Question

If x is complex, the expression (x2+34 x-71/x2+2 x-7) takes all values which lie in the interval (a, b), find the values of a and b (A) a=-1, b=1 (B) a=1, b=-1 (C) a=5, b=9 (D) a=9, b=5

Tardigrade Admin · Accepted Answer

Here we have to find range of (x2+34 x-71/x2+2 x-7)=y (Let) Then, x2+34 x-71=x2 y+2 x y-7 y ⇒ x2(y-1)+x(2 y-34)+(71-7 y)=0 As x is complex, discriminant of above equation, D ≤ 0 ⇒ (2 y-34)2-4(y-1)(71-7 y) ≤ 0 ⇒ 5 ⇒ (a, b) ≡(5,9)

Q. If $x$ is complex, the expression $\frac{x ^{2} + 34 x - 71}{x ^{2} + 2 x - 7}$ takes all values which lie in the interval $(a, b)$ , find the values of $a$ and $b$

$a = - 1, b = 1$

$a = 1, b = - 1$

$a = 5, b = 9$

$a = 9, b = 5$

Q. If x is complex, the expression x2+2x−7x2+34x−71​ takes all values which lie in the interval (a,b), find the values of a and b

a=−1,b=1

a=1,b=−1

a=5,b=9

a=9,b=5

Here we have to find range of x2+2x−7x2+34x−71​=y (Let) Then, x2+34x−71=x2y+2xy−7y ⇒x2(y−1)+x(2y−34)+(71−7y)=0 As x is complex, discriminant of above equation, D≤0 ⇒(2y−34)2−4(y−1)(71−7y)≤0 ⇒5⇒(a,b)≡(5,9)

Q. If $x$ is complex, the expression $\frac{x ^{2} + 34 x - 71}{x ^{2} + 2 x - 7}$ takes all values which lie in the interval $(a, b)$ , find the values of $a$ and $b$

$a = - 1, b = 1$

$a = 1, b = - 1$

$a = 5, b = 9$

$a = 9, b = 5$