solution of the equation

Question

Determine the nature of the solutions of the equation:

5x^2-6x=-9

 

a)Two real solutions

b) No solutions

c)One real solution

d)two solutions with imaginary parts 

Answer 1

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.

Answer 2

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?

Answer 3

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.