Question

Solve: (2x²-3x+1)(2x^2+5x+1)=9x^2
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Answer 1

Step-by-step explanation:

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If  (2x2-3x+1)(2x2+5x+1) =9x2, then eqn has

a)     Four real roots

b)    Two real and two imaginary

c)     Four imaginary roots

d)    none

8 years ago

Answers : (1)

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