Search 73,897 tutors
FIND TUTORS
Ask a question
0 0

factor 2x^2+x-14

Tutors, please sign in to answer this question.

3 Answers

2 X^2 + X - 14 
 
 
2 ( X^2 + 1/2 X - 7)         
 
   Should factor to :
 
 2 ( X + a) ( X+b)    / in such a way that  a.b = -7   a+ b = 1/2 , there is no rational numbers that that
 
                                 meet that criteria , so factor it with completing the square.
 
2 ( X^2 + 1/2 X + 1/16 - 1/16 - 7 ) =
 
2[ ( X + 1/4 ) ^2 - 113/16) ] =
 
2  ( X + 1/4 - √113/4) ( X + 1/4 + √113/4) =
 
2 ( X +1/4 + √(113/16)( X + 1/4 -(√113/16 )
 
2 ( X + ( (1 + √(113)/4) ( X + (( 1 - √113)/4)
This can be done most easily with the quadratic equation
(1/ (2*a) )*( -(b) ± √(b^2 - 4*a*c) )
 
where our original expression is interpretted
 
ax^2 + bx + c
 
            = 2x^2 + x - 14
and so a=2, b=1, and c=-14.

Comments

To extend my solution, we have:
 
(1/4) * (-1 ± √(12- 4*2*(-14)) )
 
= (1/4) * (-1 ± √(1 + 112) )
 
= (1/4) * (-1 ± √(113) )
 
= -1/4 ± √(113)/4 = x
 
which is irrational. So, using this knowledge and our knowledge of the leading coefficient being 2, we have the solution:
 
(leading coefficient)*(first zero)*(second zero)
 
or
 
2*(x + 1/4 + √(113)/4)*(x + 1/4 - √(113)/4)
 
I believe that Parviz failed to properly evaluate in his last two steps, which I believe is just a error in the parenthesis placement, an easy mistake when typing. Ebenezer evaluated 2x^2 + x + 14, demonstrating how much a slight change can effect a solution.
2x2 + x - 14
 
Using the quadratic formula;
 
x =   -b ± √ (b2 - 4ac)    
             2a
 
where a = 2, b = 1 and c = 14
 
x =   -(1) ± √ ((1)2 - 4(2)(14))
                        2(2)
 
x =  -(1) ± √ (1 - 112)
                    4
 
x = -(1) ± √(-111)
               4
 
x = -(1) ± 10.54
              4
 
x = -(1) + 10.54
              4
or
x = -(1) - 10.54
              4
 
x = 9. 54    or -11.54
        4               4
 
x = 2.39 or - 2.89

Comments

Hi Ebenezer
 
   2X^2 + X -14
 
    b^2 - 4 ac = 1^2 - 4 ( 2) ( -14) = 1 +112 = 113

Woodbridge algebra 1 tutors