Question 843009: Is this incorrect ^3x + 1 = 3 + ^x4 and if so what is the answer.
Found 2 solutions by mathhelper123, josgarithmetic:Answer by mathhelper123(14) (Show Source): You can put this solution on YOUR website! symbols are missing, you'll have to repost Answer by josgarithmetic(39631) (Show Source): You can put this solution on YOUR website! That is incorrect. The exponent needs a base; both exponents each need a base. The 3x and the x4 are ambiguous in your expression along with the missing bases, since we do not know if you want to x to be part of the exponent or one of the factors of the term; or if the 4 is a factor of the term or is part of the x exponent.
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Actual equation was to be
Some algebra steps bring that to .
Use synthetic division to check for rational roots on the polynomial ; those divisions are not shown here, but remainders occurred upon testing for 1, -1, 2, and -2. NO RATIONAL ROOTS.
According to the Remainder and the Factor Theorems, there are now four known points for the function, .
Those points are f(1)=2, f(-1)=4, f(2)=6, and f(-2)=26.
As ordered pairs, in order from left to right for x,
(-2, 26) (-1, 4) (1, 2) (2, 6)
There are or is a upper and lower bounds test which may give more information, such as maybe the left and right behavior. You might also try testing using Descartes' Rule of Signs to see if there may be some real roots or zeros, which may be irrational.
You could also use a graphing calculator just to get a quick and precise picture of the graph.
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NOTE that you should expect up to four complex roots.