Question

Type the correct answer in each box. Use numerals instead of words. 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 _______ .

Answer 1

-1 ± 3i√6

Explanation:

Please write this quadratic equation as follows: x^2 + 2x + 7 = 21. The " ^ " indicates exponentiation.

The coefficients of this quadratic are 1, 2, 7.

Thus, the "discriminant" b^2 - 4(a)(c) is (2)^2 - 4(1)(7), or 4 - 28, or -24.

Because the discriminant is negative, this quadratic has two different complex roots:

-b ± √[ discriminant ] -2 ± 2i√6

x = --------------------------------- = ----------------- = -1 ± 3i√6

2a 2