Question

Solve 2x2 + 3x + 5 = 0. Round solutions to the nearest hundredth.

x ≈ −2.14 and x ≈ 0.64 <------- MY ANSWER

x ≈ −0.64 and x ≈ 2.14

x ≈ −4.28 and x ≈ 1.28

No real solutions

Answer 1

@phi am i correct?

Answer 2

you have to use the quadratic formula

( -b ± sqrt( b*b - 4 a c) ) /(2a)

what do you get for what goes inside the square root ?

Answer 3

in other words, what is b*b - 4*a*c

Answer 4

9 - 4 * 2 * 5 = 9 - 40 = -31

Answer 5

yes, and do you know how to take the square root of a negative number ?
See http://www.regentsprep.org/Regents/math/algtrig/ATO6/SquareRootLes.htm

the short answer is you get an imaginary number (you get "complex numbers")

and as you can guess, complex or imaginary numbers are not REAL numbers

so what do you think the answer is for this question ?

Answer 6

Also, if you tried x= -2.14 in the equation:

2* (-2.14)^2 + 3* -2.14 + 5=

type that into google and it comes up with 7.73... which is not 0. so it is not the answer.

Answer 7

is it \[- \sqrt{31}\]

Answer 8

\[ - \sqrt{31} \cdot -\sqrt{31} = 31 \]
the 2 minus signs make a plus.
the square root of -31 is a bit more mysterious
\[ \sqrt{-31} = i \sqrt{31} \]
where i is short for \( \sqrt{-1} \)


the roots for this problem are
x= -0.75 + 1.39 i
x = -0.75 - 1.39 i

these are complex numbers, and you have not studied them yet (I don't think)

Answer 9

I would examine how I got choice A for the answer and figure out how not to do the same thing again, because whatever you did was not correct.

Answer 10

so then what would be the answer?

Answer 11

@phi

Answer 12

No real solutions?