Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -9x2 + 9x + 5.

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -9x2 + 9x + 5.

{–1.80, 1.80}

{-9, 9}

{–1.00, –0.56}

{–0.40, 1.40}

Answer 1

JO:

 

f(x) = 0 is -9x² + 9x + 5 = 0, which can be written as 9x² - 9x - 5 = 0.  The roots of a quadratic equation ax² + bx + c = 0 are given by the formula

 

{- b (+ or -) sqrt [b² - 4 a c]} / 2 a   Here, a = 9, b = -9 and c = -5.

 

{- b (+ or -) sqrt [b² - 4 a c]} / 2 a = {9 (+ or -) sqrt [ 81 - 4 (9) (-5)]} / 2(9)

                                                   

                                                   = { 9 (+ or -) sqrt [81 + 180]} / 18

 

 sqrt ( 261) = 16.155 (to 3 decimals)

 

(9 +  16.155) / 18 = 1.397 (to 3 decimals)

 

(9 - 16.155) / 18 =  -0.397 (to 3 decimals)

 

ANSWER {-0.40, 1.40} is the closet possible.

 

Dr. G.