Probability
Quadratic with Repeated Roots — Probability
nta_pyq_2024_apr
Grade 12
Question:
The coefficients $a,b,c$ in the quadratic equation $ax^2+bx+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$. The probability of this equation having repeated roots is:
$\dfrac{1}{128}$
$\dfrac{1}{64}$
$\dfrac{3}{256}$
$\dfrac{3}{128}$
Step-by-Step Solution
Key Concept: Repeated roots: $D=b^2-4ac=0$, i.e. $b^2=4ac$. Total outcomes $=8^3=512$. Count favourable $(a,b,c)$.
8 valid triples. $P=8/512=1/64$.
Correct Answer: 2