Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -4x^2 + 2x + 6

Question

Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -4x2 + 2x + 6.

a.{–1.00, 1.50}

b.{-4, 2}

c.{–0.50, –1.50}

d.{–0.67, 0.33}

Answer 1

 

This is a multiple-choice question - the type you find on standardized tests like the SAT.  Your approach should be to answer the question as quickly as possible without worrying about understanding details.

 

Rule #1:  On a multiple-choice question, your first step is not to work the problem.   

 

The first step is to eliminate as many answers as possible, and in this case it's sufficient.

 

The answer is (a) for the following reasons:

 

-1 is a root, which can be shown by substitution.  

-4 , -.5 and -.67 are clearly not roots - do a rough estimate in your head.

 

So the only possible answer is a.

 

Remember, on a standardised test (or any multiple-choice question like this) your goal is to select the right answer, and not to prove you can work the problem!  Just select the right answer, then go on to the next problem!  

 

Never take any problem personally on a standardized test - for example, if you feel shaky about your ability to work a problem - don't let that enter into the equation. Just use what you know.

 

This approach works really well on multiple-choice tests because most test-writers are lazy and don't take time or don't know how to make up credible alternative answers.  

Answer 2

f( x ) = -4 X^2 + 2X + 6 =0

 

        = - 2X^2 + X + 3 = 0

 

        = - ( 2X^2 - X -3) =0

 

        =  - ( 2X^2 +2X - 3x -3)

 

        = - ( 2X( X +1) -3( X +1) =0

 

        = -( X + 1 ) ( 2X - 3 )

 

          X + 1  = 0   X = -1     2X -3 = 0    X = 3/2

 

a. is correct answer.