x^2-15x+54=155 solving by rational root theorem, descartes rule of signs, and the factor theorem.

Question

solving by rational root theorem, descartes rule of signs, and the factor theorem.

Answer 1

x^2 -15x +54=155... x^2 -15x -101=0... me yuz quadratik formula tu get roots=20.0399362 & -5.0399362... b^2-4ac=629, root(629)=25.079872408... root/2a=12.53993620398

Answer 2

x^2-15x-101=0

Positive: +-- = 1

Negative: ++- =1

Imaginary: 0

from rational root theorem candidates are: +/-101 and +/-1

but none of them satisfy the given equation therefore there are no rational roots and no imaginary roots,

hence we can find the irrational roots using quadratic formula.

and on applying quadratic formula we get:

x = 1/2 (15 - sqrt(629)) or 1/2 (15 + sqrt(629))