SOLUTION: solve the equation in real # system
x^3-3/4x^2+31/4x+2=0
real solutions of the equation are x=?
dont see why my tutor i was assigned cant do these, please help
please sho
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Question 641616: solve the equation in real # system
x^3-3/4x^2+31/4x+2=0
real solutions of the equation are x=?
dont see why my tutor i was assigned cant do these, please help
please show work
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Multiply EVERY number by the LCD 4 to go from
x^3-3/4x^2+31/4x+2=0
to
4x^3-3x^2+31x+8=0
Now use the rational root theorem to list out all of the possible rational roots.
The list of all possible rational roots are
It turns out that is the only rational root. You find this out by plugging in each possible rational root and seeing if the result is 0. If it is 0, then you have a rational root.
So or is a factor. Use polynomial long division to get
Now set the quotient equal to zero and solve for x (using the quadratic formula)
a = 1, b = -1, c = 8
That last line has a negative radicand, which will lead to 2 imaginary or complex solutions (which are NOT real solutions)
So there is only one real solution and it is
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