SOLUTION: Use the quadratic formula to solve 2x^8 - 7x^4 - 3 = 0. Write your answer correct to 3 significant figures.

Algebra ->  Test -> SOLUTION: Use the quadratic formula to solve 2x^8 - 7x^4 - 3 = 0. Write your answer correct to 3 significant figures.      Log On


   

Question 1186256: Use the quadratic formula to solve 2x^8 - 7x^4 - 3 = 0. Write your answer correct to 3 significant figures.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is 2x^8 - 7x^4 - 3 = 0.

this is equivalent to:

2 * (x^4) ^ 2 - 7 * (x^4) ^ 1 - 3 = 0

if you replace x^4 with y, the equation becomes:

2y^2 - 7y - 3 = 0

this in standard form of ax^2 + bx + c = 0

when you replace x with y, it becomes:

ay^2 + by + c = 0

if you solve the quadratic equation using the quadratic formula, you will get:

y = 3.886000936 or y = -0.386000936

since y = x^4, solve this for x to get:

x = (3.886000936) ^ (1/4) or y = (-0.386000936) ^ (1/4).

you will find that the first option will get you x = plus or minus 1.404027859.

you will find that the second option will get you x = undefined because you can't take the even root of a negative number and get a real number as an answer.

you can get a complex number as an answer, but not a real number.

your solution becomes:

x = plus or minus fourth root of 3.886000936 which is equal to plus or minus 1.404027859.

if you graph the equation of y = 2x^8 - 7x^4 - 3, you will find that the roots are plus or minus 1.404 when rounded to 3 decimal places, as shown below.



here is the quadratic formula. 



               (-b plus or minus sqrt(b^2 - 4ac)
x =          --------------------------------------
                              2a