40 pts! Consider this quadratic equation. x^2+2x+7=21 The number of positive solutions to this equation is ____. The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is ____

Respuesta :

x2 + 2x + 7 = 21

Set it equal to zero by subtracting 21 from both sides

x2 + 2x + 7 - 21 = 21 - 21

x2 + 2x - 14 = 0

Use the quadratic equation:

x = (-b +- ( b^2 - 4ac)^1/2)/2a

In our equation a = 1, b = 2 and c = - 14

(-2 +-(4 + 56)^1/2)/2

x = -1 +- (60^1/2)/2

There is one positive solution to this equation

and it is 2.87

Hope it helps

  1. The number of positive solutions to this equation is one
  2. The approximate value of the greatest solution to the equation is 2.87

Given quadratic equation:

x² + 2x + 7 = 21

x² + 2x + 7 - 21 = 0

x² + 2x - 14 = 0

a = 1, b = 2, c = - 14

(1) The number of solutions of a given quadratic equation is determine by the discriminant.

[tex]b^2-4ac >0 \ \ (2 \ solutions)\\\\b^2 - 4ac = 0 \ \ (1 \ solution)\\\\b^2 - 4ac <0 \ \ ( zero \ solution)[/tex]

From the given values;

(2)² - 4(1 x -14) = 4 + 56 = 60

60 > 0 ( 2 solutions)

1 positive solution and 1 negative solution

Thus, number of positive solutions to this equation is one

(2) The greatest solution or positive solution to the equation is calculated as;

[tex]x = \frac{-b + \ \sqrt{b^2 - 4ac} }{2a} \\\\recall , b^2-4ac = 60\\\\x = \frac{-2 + \sqrt{60} }{2(1)} \\\\x = \frac{-2 + 7.746}{2} \\\\x = 2.873\\\\x \approx 2.87[/tex]

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