Select the approximate values of x that are solutions to f(x) = 0, where f(x) = -8x2 + 4x + 7.

Question

{–1.14, 0.57}

{-8, 4}

{–0.50, –0.88}

{–0.72, 1.22}

Answer 1

A possibly better solution to this problem, given that it may not always be multiple choice, is to actually find the zeroes of this function.

 

First you would let f(x)=-8x^2+4x+7=0

 

Now, since you were asked for an approximate answer, and this is a quadratic equation, you can use the quadratic formula, which says that the roots (the zeroes) of a function of this type (ax^2+bx+c=0) are equal to:

 

x=(-b+sqrt(b^2-4ac))/2a

and

x=(-b-sqrt(b^2-4ac))/2a

 

Plugging in a=-8, b=4 and c=7 simplifies to

 

x=(1+sqrt(15))/4

and

x=(1-sqrt(15))/4

 

Plugging these into our calculators gives the last solution set.

 

You may also be familiar with factoring quadratic equations into the form (x-n)(x-m)=0 in order to solve them. With this one, a hint that you should use the quadratic equation is that the constant term (c or 7 in this problem) is prime, that is there are no integers that you can multiply together to get seven

 

Answer 2

I don't know if you know how to graph in your calculator. This is the easiest way to evaluate any function. If you look in you're calculator you'll see it crosses the x-axis at –0.72 and 1.22. These x coordinates are where the function(f(x)) is equal to zero. You could also do the quadratic formula. 

Answer 3

Hi Jaime, to solve this problem you replace x with whatever value you want to test (for example: -1.14) and come up with what f(x) equals. If f(x) equals about 0 (the question asks for approximate), then the x value you used was a solution.  In this problem, the last set of values is the correct answer.