Question

If $2-i$ is a root of the equation $a{x}^2+12x+b=0$ (where $a$ and $b$ are real), then the value of ab is equal to

• A. 45
• B. 15
• C. $-15$
• D. $-45$
• E. 25

Answer 1

Answer: (A)

If one root is $2-i,$ then the other root will be
$2+i.$
Given equation is
$a{x}^2+12x+b=0$
$\therefore$ $2-i+2+i=\frac{-12}{a}$
$\Rightarrow$ $a=-3$ and $(2-i)(2+i)=\frac{b}{a}$
$\Rightarrow$ $5=\frac{b}{-3}\Rightarrow b=-15$
$\therefore$ $ab=-3\times (-15)=45$