Find the zero of this function P(x)=x^3-4x^2+2x+3?

Question

the answer is 1 plus or minus the square root or 5 over 2. Please explain your answer step by step

Answer 1

By inspection we see P(3)=0
dividing P(x) over (x-3) we have
P(x)=(x-3)(x^2-x-1)
we come to a quadratic equation with two distinct real roots:
(1+sqrt(5)/2)
(1-sqrt(5)/2)
can you see the golden ratio here?

PS. just 4 inspections was needed at first:
P(1) P(-1) P(3) P(-3)
The 3rd was successful.

Otherwise we must use cosines in Casus irriducibility.

Answer 2

Actually, your answer is wrong.... Because this is a third degree ploynomial, you have 3 zeros.

Zeros are where this function p(x) becomes zero. Graphically, this is where the line crosses the X axis.

So, to find this, you find 0=x^3-4x^2+2x+3

One of the way you can do this, is to use a graphic calculator and find the first zero, which happens to be X=3. Then, you know, one of the condition to make this equation true is to make x-3 = 0.

Knowing this, you can divide the whole equation by x-3 and get a second degree polynomial. Then it is a simple matter of solving the polynomial.

Good luck

Answer 3

This is a cubic function, which means it will cross the x axis three times when graphed. If you have a graphing calculator it is a simple matter. Just hit the y= button...when it comes up type in the equation just like you did on this screen. hit the graph button on the upper right hand side of your calculator. When the function graphs you will see the cubic curve. You can hit the "trace" key (usually to the left of the graph button) on your calculator and move to the left and right. when you get to the point where it is touching the x axis this is one of your zero's (or solutions) there are three of them. x= -0.6, x=1.6, and x=3 for this equation. After you find the "zeros" you must plug each one back in to the original equation (substituting for x each time) to see if it does in fact equal zero, if it does it is a real solution....if it doesn't equal zero then it is not a real solution... hope this helps! tes (your answer is not incorrect as indicated by someone earlier, it is just incomplete, the answer is 3 and 1 +/- sq.5 over 2)

Answer 4

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Answer 5

Mr. smart. i don't think u ever gonna get a answer for that. its looks complicated

Answer 6

#@!$%*+$#*@!^$