Step-by-Step Solution
Key Concept: For $x^2 + bx + c$, if $b > 0$ and $c > 0$, sum of zeroes $\alpha + \beta = -b < 0$ and product $\alpha \beta = c > 0$, so both zeroes must be negative.
Stepwise Solution:
Here $a=1, b=99, c=127$. Product of zeroes $\alpha \beta = 127 > 0$, so both zeroes have the same sign. [0.5 Mark]
Sum of zeroes $\alpha + \beta = -99 < 0$. Since product is positive and sum is negative, both zeroes must be negative. [0.5 Mark]
Marking Scheme:
• Analyzing product of zeroes: 0.5 Mark
• Analyzing sum of zeroes to determine signs: 0.5 Mark
Correct Answer: Both negative