Question

which of the following are solutions to the equation below?
Check all that apply.
2x^2+5x+8=6
A. -2
B. -1 ]
C. -1/2
D. 1/2
E. 1
F. 2

Answer 1

Both A and C would be solutions to the equation.

In order to solve for this you must first get the equation equal to 0. 

2x^2+5x+8=6 ----> subtract 6 from both sides
2x^2 + 5x + 2 = 0

Now knowing this we can use the coefficients of each one in descending order of power as a, b and c. 

a = 2 (because it is the coefficient to x^2)
b = 5 (because it is the coefficient to x)
c = 2 (because it is the end number)

Now we can plug these values into the quadratic equation. 

$\frac{-b +/- \sqrt{b^{2} - 4ac } }{2a}$

$\frac{-5 +/- \sqrt{5^{2} - 4(2)(2) } }{2(2)}$

$\frac{-5 +/- \sqrt{9} }{4}$

$\frac{-5 +/- 3 }{4}$

$\frac{-5 + 3 }{4}$ or -1/2 for the first answer

$\frac{-5 - 3 }{4}$ or -2 for the second answer