The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring.
What is the constant of the quadratic expression in this equation?
x2 + x + ___ = 0
-420
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The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring.
What is the constant of the quadratic expression in this equation?
x2 + x + ___ = 0
-420
To find the constant of the quadratic expression in the equation related to the product of two consecutive integers that equals 420, we first label the smaller integer as ( x ). The two consecutive integers can then be represented as ( x ) and ( x + 1 ).
The equation based on the product is:
[
x(x + 1) = 420
]
Expanding this gives:
[
x^2 + x – 420 = 0
]
In the standard form ( x^2 + x + c = 0 ), ( c ) represents the constant term. From our equation, we see that the constant term ( c = -420 ).
So the correct answer is:
-420
This indicates that the constant in the rewritten quadratic expression that represents the product of the integers is -420.