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Question 1: Identify the number and type of solutions for the equation x2 − 7x + 3 = 0. Answers: 2 real, 1 real, 1 nonreal complex, 2 nonreal complex Question 2: Identify the number and type of solutions for the equation 3x2 + 2x + 9 = 0. Answers: 1 nonreal complex, 2 real, 1 real, 2 nonreal complex

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Answer:

below

Step-by-step explanation:

[tex]x^{2} -7x + 3[/tex]

this is a quadratic equation so we will use the quadratic formula to solve it

  • a = 1
  • b = -7
  • c = 3

The quadratic formula:

  • b² - 4ac = (-7)²-4*1*3 = 37
  • 37 is a positive number so the equation has two solutions

[tex]x = \frac{-b + / - \sqrt{37} }{2a}[/tex] ⇒ [tex]x = \frac{7 + / - \sqrt{37} }{2}[/tex]

                      ⇒ [tex]\left \{ {{x=0.45} \atop {x=6.54}} \right.[/tex]

The solutions are 2 real numbers