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

Step-by-step solution

Here we have to find range of ( x^2+34 x-71 x^2+2 x-7 =y ) (Let) Then, ( gathered x^2+34 x-71=x^2 y+2 x y-7 y x^2(y-1)+x(2 y-34)+(71-7 y)=0 gathered ) As (x ) is complex, directriminant of above equation, ( array ll & D 0 & (2 y-34)^2-4(y-1)(71-7 y) 0 & 5 < y < 9 & (a, b) (5,9) array )