Question

If $1,2,3$ are the roots of the equation $x^4+a{x}^2+bx+c=0$ then the value of $c$ is :

• A. $18$
• B. $-36$
• C. $30$
• D. $32$

Answer 1

The correct option is B $-36$

$1,2$ and $3$ are the roots of given equation,
$\therefore a+b+c=-1.....\left(i\right)$
$4a+2b+c=-16.....\left(ii\right)$
$9a+3b+c=-81....\left(iii\right)$

$\left(iii\right)-\left(i\right)$
$8a+2b=-80$..........$\left(iv\right)$
$\left(ii\right)-\left(i\right)$

$3a+b=-15$..............$\left(v\right)$
Solving $a=-25$ & $b=60$
putting value of $a$ & $b$ in eq. $\left(i\right)$, we get
$c=-36$

Hence, option (b) is correct.