The product of two consecutive positive integers is $306$. The quadratic equation representing this scenario is:
(a) $x^2 + x - 306 = 0$
(b) $x^2 - x - 306 = 0$
(c) $x^2 + 2x - 306 = 0$
(d) $x^2 - 2x + 306 = 0$
Step-by-Step Solution
Key Concept: $x(x + 1) = 306 \Rightarrow x^2 + x - 306 = 0$.
$x(x + 1) = 306 \Rightarrow x^2 + x - 306 = 0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Forming equation $x^2 + x - 306 = 0$: 1.0 Mark
Correct Answer: $x^2 + x - 306 = 0$