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 $