F(X) = x^3 - 343x^3

Question

Find all the X-intercepts of each polynomial.

Answer 1

F(X) = x^3 - 343x^3

 

Adding your like terms since both have variable x³

F(X) = -342x³

For x intercepts set this equal to zero

-342x³ = 0

This crosses the x axis at x=0 and F(X) = 0

So the x-intercept is (0,0)

 

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If, as Alan G. surmised, your homework had a misprint

and the polynomial is supposed to be

x³- 343

You may wonder if this is the difference of 2 cubes.

³√343 = 7   or  7³ = 343  so your polynomial is:

 

x³ - 7³

The formula for factoring the difference of

two cubes is a³-b³ = (a-b)(a²+ab+b²)

In this case a=x, b=7

 

x³-7³ = (x-7)(x²+7x+49)

We can see that one x-intercept is at x=7 so (7,0) is one intercept

 

We need to check the quadratic x²+7x+49 = 0

Using the quadratic equation we get

 

x = [-7 ±√(49-4(49))]/2

 

x= [-7 ±√(-147)]/2

 

x = [-7 ± i√147]/2

As can be seen, both roots of this quadratic are

complex numbers, and are "imaginary".

This means the only real x-intercept is the one

already determine... (7,0)

Answer 2

Is the polynomial correct? I wonder if the second term is actually -343 and not -343x³.

 

Let me know and I will send an answer or hint to help you.