Probability
Quadratic with One Root Bigger — Probability
nta_pyq_2024_apr
Grade 12
Question:
The coefficients $a,b,c$ in the quadratic equation $ax^2+bx+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger than the other is $p$, then $216p$ equals:
Step-by-Step Solution
Key Concept: "One real root bigger than the other" means two distinct real roots: $D>0$, i.e. $b^2>4ac$. Total $=6^3=216$. Count $(a,b,c)$ with $b^2>4ac$.
38 favourable cases. $216p=38$.
Correct Answer: 3