Quadratic Challenge

Algebra Level 3

Consider this equation: where it is defined. Compute a+b.


The answer is 7.

William Isoroku by William Isoroku , 25, USA

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2 solutions

for the left hand side to simplify to the right hand side, the numerator must be (x+7) multiplied by another linear expression. which means x=-7 is a solution for the numerator. use factor theorem for the numerator and substitute x=-7. you get 49-7a-7b=0. so a+b=7.

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Works too.

William Isoroku - 6 years, 8 months ago
William Isoroku
Aug 21, 2014

There's a few ways of doing this problem. Consider x+7 to be one factor of the left-hand numerator and x+11 to be the left-hand denominator. Then it simplifies to x=-7 and x=-11 by the zero-product property. By substituting these 2 values to the matching equations will give us 2 linear equations with 2 variables. Simply solve for the variables and add.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

for the question that is asked, it is enough to substitute it in the numerator alone and get the value of a+b

Swamynathan Mahesh - 6 years, 8 months ago

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