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(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.

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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.

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(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

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