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solution of the equation

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3 Answers

5X^2 -6X + 9 =0
 
   Test :
 
 
 b^2 - 4ac= 6^2 - 4 ( 5) ( 9) = 36 - 180 = - 144
 
   Discriminant is negative, therefore 2 complex roots. Roots with Imaginary parts.
   
 So, you know which answer you should mark as the correct answer.
5x2 - 6x = -9
 
Put the equation in standard form:
 
5x2 - 6x + 9 = 0
 
Use the quadratic formula to find the values of x:
 
x = (-b/2a) ± (1/2a) √(b2-4ac)
 
For this problem, a = 5, b = -6, c = 9:
 
x = (6/10) ± (1/10)√[(-6)2-4(5)(9)]
 
x = (3/5) ± (1/10)√(36-180)
 
x = (6/10) ± (1/10)√(-144)
 
Can you finish it from here?

Comments

Both solutions have an imaginary part (√-144 = 12i), so D is correct.
If the equation is written correctly above, then the solution looks like this:
 
5x-6x=-9
-x=-9     (Combining like terms)
x=9       (mult both sides by -1)
Therefore it has one real solution.