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# If  (2x2-3x+1)(2x2+5x+1) =9x2, then eqn has a)     Four real rootsb)    Two real and two imaginaryc)     Four imaginary rootsd)    none

9 years ago

Dear pooja,

correct option is a)

solution

(2x2-3x+1)(2x2+5x+1) =9x2

divide the equation by x^2 where x not equal to 0

(2x-3+1/x)(2x+5+1/x) = 9

let  2x+1/x = y  put in the equation

(y-3)(y+5) = 9

y2+2 y - 24 = 0

solving the equation we get  y = -6 and y = 4

so we get

2x+1/x = -6        and

2x+1/x = 4      we get

2x2+6x+1=0    finding discriminant we get it as  +ve so 2 real roots

 2x2-4x+1=0 and again finding discriminant we get it as +ve so 2 real roots   so the total of 4 real roots

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