Question

If $2x^5+ax^4-12x^3+bx^2+x+c=0$ is reciprocal equation of class one, find sum of rational roots.

• A. $-\frac{1}{2}$
• B. $-\frac{7}{2}$
• C. $\frac{1}{2}$
• D. $\frac{7}{2}$

Hint:

Reciprocal equations always have symmetric roots.

Answer 1

The Correct Option is B

Step 1: Reciprocal condition: \[ P(x)=x^5P(1/x) \]
Step 2: Compare coefficients: \[ c=2,\quad b=a \]
Step 3: Rational roots occur in reciprocal pairs: \[ \alpha+\frac{1}{\alpha} \]
Step 4: Sum of roots: \[ -\frac{a}{2} \]
Step 5: From symmetry: \[ a=7 \]
Step 6: \[ \text{Sum}=-\frac{7}{2} \]