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3 years ago

5

2/3x=4 what does x equal?

1 answer:

Bogdan [553]3 years ago

4 0

Answer:

0=6

Step-by-step explanation:

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Answer:

The Factored form is

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Step-by-step explanation:

Given;

$f(x)=x^{3} -7\times x^{2} +2x+4$

To solve for x we factorize the right side of

$f(x)=x^{3} -7\times x^{2} +2x+4$

Let Substitute x for various values to check whether remainder is zero.

$f(1)=1^{3} -7\times 1^{2} +2\times 1+4$

Hence $x-1$ is a factor of the function.

Do synthetic division to find the quotient

$1$ $1$ $-7$ $2$ $4$

$1$ $-6$ $-4$

_____________________

$1$ $-6$ $-4$ $0$

We get remainder 0 and quotient as,

$x^{2} -(6\times x)-4$

By using Quadratic Formula;

$x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}$

Plug 'a' , 'b' and 'c' value from $x^{2} -(6\times x)-4$ equation,

$x=\frac{-(-6)\pm\sqrt{-6^{2}-(4\times1\times -4 )} }{2\times1}$

$x=\frac{6\pm\sqrt{36+16 } }{2}$

$x=\frac{6\pm\sqrt{52} }{2}$

$x=3+\sqrt{13}$ and $x=3-\sqrt{13}$

The values of 'x' are $1$ , $3+\sqrt{13}$ and $3-\sqrt{13}$

So the Factored form is

$f(x)=(x-1)(x-3-\sqrt{13} )(x-3+\sqrt{13} )$

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