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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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.

5x^{2} - 6x = -9

Put the equation in standard form:

5x^{2} - 6x + 9 = 0

Use the quadratic formula to find the values of x:

x = (-b/2a) ± (1/2a) √(b^{2}-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?

Peter Y. | Peter's Profile: Math TutoringPeter's Profile: Math Tutoring

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.

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