Question

Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21

Answer 1

Complete question is;

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:

The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is 2.87.

Step-by-step explanation:

We are given the quadratic equation as;

x² + 2x + 7 = 21

Subtract 21 from both sides to give ;

x² + 2x + 7 - 21 = 0

x² + 2x - 14 = 0

Using quadratic formula, we cam find the roots of the equation.

x = [-b ± √b² - 4ac]/2a

Plugging in the values;

x = [-2 ± √(2² - 4(1*-14))]/2(1)

x = [-2 ± √(4 + 56)]/2

x = [-2 ± √60]/2

x = - 4.87 or 2.87

Thus, this equation has only one positive solution which is the greatest.

Thus, greatest solution is 2.87