Question

If one root of $ax^2 - bx + a = 0$ is $6$, then $\frac{b}{a}$ is:

• A. \( \frac{1}{6} \)
• B. \( \frac{11}{6} \)
• C. \( \frac{37}{6} \)
• D. \( \frac{6}{11} \)
• E. \( \frac{6}{37} \)

Hint:

Substitution is the fastest method when one root is directly given.

Answer 1

The Correct Option is C

Concept: If \( x = r \) is a root, substitute into equation.

Step 1: Substitute root \( x=6 \).
\[ a(6)^2 - b(6) + a = 0 \] \[ 36a - 6b + a = 0 \] \[ 37a = 6b \]

Step 2: Find ratio.
\[ \frac{b}{a} = \frac{37}{6} \]