Binomial Theorem
Coefficients in Trinomial — Finding Parameters
nta_pyq_2023_apr
Grade 11
Question:
Let $(a+bx+cx^2)^{10}=\displaystyle\sum_{i=0}^{20} p_i x^i$, $a,b,c\in\mathbb{N}$. If $p_1=20$ and $p_2=210$, then $2(a+b+c)$ is equal to
Step-by-Step Solution
Key Concept: Coeff of $x$: $10a^9b=20\Rightarrow a^9b=2$. Coeff of $x^2$: $45a^8b^2+10a^9c=210\Rightarrow 9a^8b^2+2a^9c=42$.
$a=1,\ b=2,\ c=3$. $2(1+2+3)=12$.
Correct Answer: 3