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
- The number of positive solutions to this equation is one
- 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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