Question

Please advise! I will Fan and Metal!

A system of equations consists of y = x3 + 5x + 1 and y = x. The equations are equal at approximately x = -0.25, -0.5, 0.5, 0.25

Answer 1

When the two equations are equal you will have:\[x^3+5x+1=x\]agreed?

Answer 2

since both \(y\) values must be the same when these equations are equal

Answer 3

Ok, I see what you are saying. So would I plug in each of the numbers to see if the solution matches?

Answer 4

You can first simplify this by subtracting \(x\) from boh sides to get:\[x^3+4x+1=0\]Then notice that this can be factored as follows:\[x(x^2+4)+1=0\]If we now subtract \(1\) from both sides we get:\[x(x^2+4)=-1\]The terms inside the braces, i.e. \((x^2+4)\) can never be negative.
This therefore tells us that \(x\) must be negative for \(x(x^2+4)\) to give us a negative result - understand?

Answer 5

I think I do. So the end number will be a negative?

Answer 6

yes - so we now it can only be one of the negative choices. Now just try each one and see which one works

Answer 7

ok would it be -0.5 ?

Answer 8

try pluggin in -0.5 into:\[x^3+4x+1\]Then try it with -0.25

see which one gives you a result that is closest to zero - that will be your answer.

Answer 9

Oh! I got it! it is -0.25! ok I was over thinking it haha

Answer 10

Thank you!

Answer 11

correct, and yw :)