f (x) question

Question

Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -7x^2 + 9x + 5

 

A. {–1.40, 1.80}
B. {-7, 9}
C. {–1.29, –0.71}
D. {–0.42, 1.70}

 

explain the answer so I can understand, I am lost on this one. thanks

Answer 1

With so many choices that are not integers, try the quadratic equation where a = - 7, b = 9 and c = 5

 

The discriminant, b² - 4ac = 81 - 4(- 7)(5) = 221, which is positive, so the function has real roots.

 

 

x = [- b (+/-)sqrt(221)]/2a

 

x = [- 9 (+/-)sqrt(221)]/(- 14)

 

x = {- .42, 1.70}  That is choice D.

Answer 2

0 = -7x² + 9x + 5

 

Quadratic formula time

(-b ± √(b² - 4ac)) / 2a

(-9 ± √(9² - 4 * -7 * 5)) / (2 * -7)

(-9 ± √(81 + 140)) / -14

(-9 ± √(221) / -14

221 = 17 * 13, so no easy square roots. We can round it to 14.866

(-9 ± 14.866) / -14

 

5.866 / -14 ≈ -0.419

-23.866 / -14 ≈ 1.70

 

These answers are close to choice D.