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43 votes
43 votes
Consider this quadratic equation.

x2 + 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

User VividD
by
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1 Answer

24 votes
24 votes

Answer:

1 positive solution (and 1 negative)

the greatest solution is about 2.87

Explanation:

so, it is

x² + 2x + 7 = 21

x² + 2x - 14 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 2

c = -14

x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =

= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =

= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =

= -1 ± sqrt(15)

x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87

x2 = -1 - sqrt(15) = -4.872983346...

User Xiao Hanyu
by
2.8k points