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 May 7 | Theresa from Jackson, NJ | 3 Answers | 0 Votes Mark favorite Subscribe Comment
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. May 7 | Parviz F. Comment
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? May 7 | Philip P. Comment Comments So the answer is D right ? May 7 | Theresa from Jackson, NJ Both solutions have an imaginary part (√-144 = 12i), so D is correct. May 7 | Philip P. Comment
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. May 7 | Peter Y. Comment
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