SOLUTION: The solution set of the equation {{{ x^2+sqrt( 2 )x=1/2 }}} consists of: A) one negative rational number. B) one positive integer and one negative rational number. c) two

Algebra ->  Functions -> SOLUTION: The solution set of the equation {{{ x^2+sqrt( 2 )x=1/2 }}} consists of: A) one negative rational number. B) one positive integer and one negative rational number. c) two      Log On


   

Question 1006242: The solution set of the equation +x%5E2%2Bsqrt%28+2+%29x=1%2F2+ consists of:
A) one negative rational number.
B) one positive integer and one negative rational number.
c) two irrational numbers.
D) two non real complex numbers.
E) two positive rational numbers.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i would say 2 irrational numbers.

your eqaution is:

x^2 + sqrt(2)x = 1/2

subtract 1/2 from both sides of the eqution to get:

x^2 + sqrt(2)x - 1/2 = 0

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

a = 1
b = sqrt(2)
c = -1/2

using the quadratic formula, you get:

x = -1 - sqrt(2)/2 or x = 1 - sqrt(2)/2

anything with a sqrt(2) in it is going to be irrational.

the first one is negative.
the second one is positive.
they are both irrational.

looks like selection c.

my worksheet for solving the quadratic equation using the quadratic formula is shown below:

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