SOLUTION: Two numbers differs by 7. The product is less than 78.find possible range of values of smaller number

Question 1087254: Two numbers differs by 7. The product is less than 78.find possible range of values of smaller number
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let x = the smaller number
Then the larger number is x+7
Their product is less than 78:
x(x+7) < 78
x^2 + 7x - 78 < 0
In other words, we need to find the intervals where the quadratic x^2 - 7x - 78 is less than zero.
The quadratic can be factored as (x-6)(x+13), so the zeros are x=6 and x=-13
Since the leading term is positive, the parabola opens up and crosses zero at x=6 and x=-13.
So the range of values are -13 < x < 6
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