How do you factor x^2+x-3?

Question

Or can it even be factored?

Answer 1

use the quadratic equation

[-b +-  sqrt(b^2-4ac)] /2(1)

using that to answer your question

=[-(1) +- sqrt ((1)^2 - (4)*(1)*(-3))] /2(1)

=  [-(1) +- sqrt 13] /2(1)

since you have to add and subtract -2, it will yield two roots. i dont have a calculator right now so i'll have to leave the rest to you. just follow the formula and you'll be fine:)

Answer 2

Use quadratic formula or completing the square for this one

Question Number 1 :

For this equation x^2 + x - 3 = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation x^2 + x - 3 = 0 is already in a*x^2+b*x+c=0 form.

As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = 1, c = -3.

1A. Find the roots using Quadratic Formula !

  Use the formula,

    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  As a = 1, b = 1 and c = -3,

  then the value a,b and c in the abc formula, can be subtituted.

  So x1 = (-(1) + sqrt( (1)^2 - 4 * (1)*(-3)))/(2*1) and x2 = (-(1) - sqrt( (1)^2 - 4 * (1)*(-3)))/(2*1)

  Which can be turned into x1 = ( -1 + sqrt( 1+12))/(2) and x2 = ( -1 - sqrt( 1+12))/(2)

  Which make x1 = ( -1 + sqrt( 13))/(2) and x2 = ( -1 - sqrt( 13))/(2)

  We can get x1 = ( -1 + 3.60555127546399 )/(2) and x2 = ( -1 - 3.60555127546399 )/(2)

  The answers are x1 = 1.30277563773199 and x2 = -2.30277563773199

1B. Use completing the square to find the root of the equation !

  x^2 + x - 3 = 0 ,divide both side with 1

  So we get x^2 + x - 3 = 0 ,

  Which means that the coefficient of x is 1

  We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 1/2 = 0.5

  Next, we have to separate the constant to form x^2 + x + 0.25 - 3.25 = 0

  And it is the same with ( x + 0.5 )^2  - 3.25 = 0

  So we will get (( x + 0.5 ) - 1.80277563773199 ) * (( x + 0.5 ) + 1.80277563773199 ) = 0

  By opening the brackets we will get ( x + 0.5 - 1.80277563773199 ) * ( x + 0.5 + 1.80277563773199 ) = 0

  Just add up the constants in each brackets, and we get ( x - 1.30277563773199 ) * ( x + 2.30277563773199 ) = 0

  We get following answers x1 = 1.30277563773199 and x2 = -2.30277563773199

Answer 3

No, it can't be factored

Answer 4

It doesn't factor under rational numbers

You would have to use the quadratic formula to solve...

(the only factors of 3 are 1 and 3, and these can't be added / subtracted to give the middle coefficient of 1)

using the QF to find the zeros / x-intercepts (If that's really what you're trying to do)

x = [-b +/- sqrt(b^2 - 4ac)] / (2a), where

a = 1, b = 1, and c = -3

x = [-1 +/- sqrt(1 - 4(1)(-3))] / (2*1)

x = [-1 +/- sqrt(13)] / 2

x = -1/2 +/- sqrt(13) / 2