use the discriminant to determine the number and type of solutions for the following equation. 2x2 + 14x + 11 = 0 a) there are zero rational solutions b) there is one rational solution c) there are two rational solutions d) there are two irrational solutions

Hello!

The discriminant of a quadratic function is found by using this formula:

D = b² - 4ac

Once you substitute the values into the formula, there are three ways your answer can be interpreted.

1. If the discriminant is positive, then there are two rational solutions.

2. If the discriminant is negative, then there are no rational solutions.

3. If the discriminant is equal to zero, then there is only one rational solution.

Given the equation, 2x² + 14x + 11 = 0, a = 2, b = 14, and c = 11.

14² - 4(2)(11)

196 - 88 = 108

Since the discriminant, 108, is a positive integer, the answer is C, there are two rational solutions.

its two irrational solutions!

Step-by-step explanation:

I just took the test and this  was the correct answer.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.