select the approximate values of x that are solutions

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -7x2 + 9x + 5.

A. {–1.40, 1.80}

B. {-7, 9}

C. {–1.29, –0.71}

D. {–0.42, 1.70}

Answer 1

If we use the quadratic equation to solve for the roots, which is  [ -b ± √(b² - 4ac) ] / 2a

 

so, for your eqn  f(x) = -7x² + 9x + 5     

a = -7

b = 9

c = 5

 

substituting, we get  -9 ± √[9² - 4(-7)(5) ] / 2(-7)   or   -9 ± √[81 - (-140) ] / -14

 

-9/-14  ± √221/-14   or   0.642 ±  14.866/-14  

 

so our two solutions are  (0.642 + (-1.062))  and  (0.642 -  (-1.062))  

or  -0.420 and 1.704   

 

so the answer is D     (rounded to two dec places)