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Find all integers $n$ such that the quadratic $7x^2 + nx - 11$ can be expressed as the product of two linear factors with integer coefficients.

Hint: Write $7x^2 + nx - 11 = (Ax + B)(Cx + D).$

Write out all the steps and explain thoroughly. 

 Nov 19, 2020
edited by MathzSolver111  Nov 19, 2020
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7x^2  + nx - 11

 

Note  that  we have   

(7x  - 11)  (x + 1)      =    7x^2 - 11x + 7x  - 11   =   7x^2 - 4x - 11

(7x - 1)   (x + 11)     =     7x^2 -1x + 77x - 11    =    7x^2 + 76x - 11

(7x + 11) (x - 1)       =     7x^2  + 11x - 7x  - 11  =   7x^2 + 4x  -11

(7x + 1) (x - 11)   =         7x^2 - 77x  +1x - 11   =    7x^2  - 76x  - 11

 

 

cool cool cool

 Nov 19, 2020

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