Question

If $a{x}^3+b{x}^2+cx+d=0$ is a reciprocal equation of the first type, then

• A. $a=d,b=c$
• B. $a=c,b=d$
• C. $a=-d,b=-c$
• D. $a=-c,b=-d$

Answer 1

Answer: (A)

$a=d,b=c$

If $a{x}^3+b{x}^2+cx+d$ is a reciprocal equation of the first type,

We know that

$a_r=a_{n-r}$ where $a_n$ are the coefficient of the equation $f\left(x\right)$

So, as $f\left(x\right)=a{x}^3+b{x}^2+cx+d$

$a=d$ and $b=c$