Question

If the zeroes of the polynomial $ax^2 + bx + \dfrac{2a}{b}$ are reciprocal of each other, then the value of $b$ is

• A. $\dfrac{1}{2}$
• B. 2
• C. -2
• D. $-\dfrac{1}{2}$

Hint:

Use relationship between roots and coefficients: $\alpha\beta = \dfrac{c}{a}$.

Answer 1

The Correct Option is B

Given:
The polynomial is \( ax^2 + bx + \dfrac{2a}{b} \)
Its zeroes are reciprocals of each other.

Step 1: Use the relationship between zeroes
Let the zeroes be \( \alpha \) and \( \frac{1}{\alpha} \)
Then, product of roots = \( \alpha \cdot \frac{1}{\alpha} = 1 \)

Step 2: Use the formula for product of roots of a quadratic polynomial
\[ \text{Product of roots} = \frac{c}{a} = \frac{\frac{2a}{b}}{a} = \frac{2}{b} \]
Set this equal to 1 (since product of roots is 1):
\[ \frac{2}{b} = 1 \Rightarrow b = 2 \]

Final Answer:
The value of \( b \) is 2.