show that for the equation y^3 - 3y + 4 = 0 ,(adsbygoogle = window.adsbygoogle || []).push({});

one of the root lies between -3 and -2

i don't know how to show that one of the root lies between -3 and -2, but i can show that one of the root ( or more ) is smaller than - 3^(1/2), pay in mind that -3 and -2 are also smaller than -3^(1/2).

Here is my method, but it doesn't solve the question, i wrote it just for your reference so you got more idea to solve it. U help is meaningful to me, thanks you !

y^3 - 3y + 4 = (y)(y^2 - 3) + 4 = 0

so this mean in order to make the equation becomes zero,

the term (y)( y^2 - 3) must equal -4, in order word, it must less than zero...

hence it is right to write (y)(y^2 - 3) < 0

by number line method or graph method, we know that the range of y for this inequality is y < -3^(1/2) or 0 < y < 3^(1/2)

so this imply that one of the root ( or more ) is smaller than -3^(1/2).

But, this is not the correct answer, we need to show it lies between -3 and -2 , not the negative squate root of 3 !!!!

Please, any expert, if u know the method, please show me as soon as possible, u help is meaningful to me!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Polynomial inequality

Loading...

Similar Threads for Polynomial inequality | Date |
---|---|

I Splitting ring of polynomials - why is this result unfindable? | Feb 11, 2018 |

I Is there a geometric interpretation of orthogonal functions? | Jan 25, 2018 |

I Example of an Inseparable Polynomial ... Lovett, Page 371 .. | Jun 6, 2017 |

**Physics Forums - The Fusion of Science and Community**