Vectors & Algebra
Linearly dependent vectors — integral values of lambda for 2 solutions
MJAT_TS5_P1
Grade 12
Question:
**Paragraph (continued):** If the equation $t=x+\dfrac{1}{x}$ has exactly two real and distinct solutions of $x$, then the number of integral values of $\lambda$ in $[-25,15]$ is:
Step-by-Step Solution
Key Concept: Exactly 2 solutions of $t=x+1/x$ occur when $|t|>2$ (one for each of $t>2$ and $t<-2$) — actually each gives 2 solutions. Or exactly 2 when $t=\pm 2$. Need to count $\lambda$ values in $[-25,15]$ that give the right number of $t$ solutions.
$\mathbf{9}$ integral values.
Correct Answer: 9