Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

which two values of x are roots of the polynomial below?

x^2 + 5x + 9

Which Two Values Of X Are Roots Of The Polynomial Below X2 5x 9 class=

Sagot :

Answer:

The answer:

A. [tex]x= \frac{-5+ \sqrt{-11} }{2}[/tex]

F.[tex]x= \frac{-5- \sqrt{-11} }{2}[/tex]

Step-by-step explanation:

Step 1: Solve with quadratic formula

  • [tex]x_{1},2 = \frac{-b+- \sqrt{b^2}- 4ac }{2a}[/tex]
  • For [tex]a=1, b=5, c=9\\x_{1},2 = \frac{-5 + \sqrt{5^2 -4 *1 *9} }{2*1}[/tex]

Step 2: Simplify

  • [tex]\sqrt{5^2 - 4 *1 *9} : \sqrt{11} i[/tex]
  • Multiply the numbers: [tex]4*1*9 = 36[/tex]
  • [tex]i\sqrt{ 36 -5^2}[/tex] = [tex]\sqrt{-5^2 + 36} = i\sqrt{11}[/tex]
  • [tex]5^2 = 25 = \sqrt{-25 + 36}[/tex]
  • Add/subtract the numbers [tex]-25 +36 = 11 = \sqrt{11} = \sqrt{11}i[/tex]

Step 3: Separate the solution

  • [tex]x_{1} = \frac{-5 + \sqrt{-11}i}{2} , x_{2} = \frac{-5 - \sqrt{-11}i}{2}[/tex]

Esther

Answer:

[tex]\large {\textsf{A and F}}\ \implies \bold{x_1}=\dfrac{-5-\sqrt{-11}}{2},\ \bold{x_2}=\dfrac{-5+\sqrt{-11}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0.

Given polynomial: x² + 5x + 9

⇒ a = 1, b = 5, c = 9

Step 1: Rewrite to Standard Form.

⇒ x² + 5x + 9 = 0

Step 2: Substitute the values of a, b, and c into the formula.

⇒ a = 1, b = 5, c = 9

[tex]x=\dfrac{-5\pm\sqrt{\bold{5^2}-4\bold{(1)(9)}}}{\bold{2(1)}}\\\\x=\dfrac{-5\pm\sqrt{25\bold{\ - \ 4(9)}}}{2}\\\\x=\dfrac{-5\pm\sqrt{\bold{25-36}}}{2}\\\\x=\dfrac{-5\pm\sqrt{-11}}{2}[/tex]

Step 3: Separate into two possible cases.

[tex]x_1=\dfrac{-5-\sqrt{-11}}{2}\\\\x_2=\dfrac{-5+\sqrt{-11}}{2}[/tex]

Other examples:

brainly.com/question/27988150

brainly.com/question/27740685

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.