Consider the equation. show work

Question

Consider the equation 9x2 + 12x - 5=0.

(a) Find and state the value of the discriminant, b2 – 4ac. Then state whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exists. Show work.

 

 

(b) Find the exact solutions of the equation. Simplify as much as possible. Show work. You are welcome to use any of the techniques which apply and that you prefer (i.e., factoring, applying the principle of square roots, completing the square, or the quadratic formula.)

Answer 1

The procedure is

 

a X^2 + bx + c = 0

 

i.e. 9 x^2 + 12X - 5          choose 2 number is:

                                       mn = 9(- 5) , and m +n = 12    m = 15 , n = -3 is the answer.

 

  break 12 X = 15X -3X

 

   9 X^2 + 15X - 3X -45 = 0

 

   9X ( X - 5 ) - 3 ( X -5 ) =0

 

     (9X - 3 ) ( X -5 ) =0

 

     9X -3 =0   X = 1/3        X - 5 = 0     X = 5

 

 

Answer 2

Hello, thank you for taking the time to post your question!

The given quadratic equation is

9x^2 + 12x – 5 = 0, meaning that a = 9, b = 12, c = -5 for this expression

For the discriminant you can just plug in those values directly

Discriminant = 12^2 – 4(9)(-5) = 144 + 180 = 324

Since the value exceeds 0 that means that there are two different real-number solutions on this one

To find those values then for part (b) I think that it makes the most sense to use the quadratic formula or some type of technology since this one doesn’t factor neatly. When I do that I get x = 1/3 and x = -5/3 for the exact values for this quadratic!

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 3

(b) Factoring: 9x²+12x-5=0 => (3x+5)(3x-1)=0 => 3x+5=0 OR 3x-1=0, so x₁=-5/3, x₂=1/3