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The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.
We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:
x² + 1300x + 1300
= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²
= x² + 2x(650) + (650)² + 1300 - (650)²
= (x + 650)² + 1300 - 422500
= (x + 650)² - 421200.
Comparing this to (x + b)² + c, we get:
b = 650, and c = -421200.
Therefore, the value of c/b = (-421200)/650 = -648.
Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The question seems improper. The proper question is:
" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"
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