Nancyhamud42idn
Answered

Get clear, concise, and accurate answers to your questions on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

(a) Use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7
(b) What are the roots of 2x^2+4x+7 ? Show your work.

Sagot :

Sqdancefanidn

9514 1404 393

Answer:

  • 2 roots
  • x = -1 +i(√10)/2, x = -1 -i(√10)/2

Step-by-step explanation:

(a) The polynomial is degree 2, so the fundamental theorem of calculus tells you there are 2 roots.

__

(b) We can "complete the square" to find the two roots.

  2x^2 +4x +7 = 2(x^2 +2x) +7 = 2(x^2 +2x +1) +5 = 2(x +1)^2 +5

This is zero when ...

  2(x +1)^2 = -5 . . . . . subtract 5

  x +1 = ±i(√10)/2 . . . divide by 2, take the square root

  x = -1 ±i(√10)/2 . . . subtract 1

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.