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Polynomials
RD Sharma
CBSE
Grade 10

Question:

The zeroes of the quadratic polynomial $x^2 + 99x + 127$ are:
(a) Both positive
(b) Both negative
(c) One positive and one negative
(d) Equal

Step-by-Step Solution

Key Concept: If $a, b, c$ have same sign, product is positive and sum is negative, so both roots are negative.
Sum $= -99$ (negative) and Product $= 127$ (positive). Two numbers with positive product and negative sum must both be negative. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Arguing from sum $< 0$ and product $> 0$: 1.0 Mark

Correct Answer: Both negative
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