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If $2-i$ is a root of the eqn., $ax^2+12x+b$, where $a$ and $b$ are real then the value of $ab$ = ?

(A) 45 (B) 25 (C) 15 (D) -45

1 Answer

Toolbox:
  • complex roots of an equation occur in conjugate pairs.
If $2-i$ is a root of $ax^2+12x+b$, then $2+i$ is the other root.
Sum of the roots $=\large-\frac{12}{a}$$=(2+i)+(2-i)=4$
$\Rightarrow\:a=-3$
Product of the roots $=\large\frac{b}{a}$$=(2+i)(2-i)=5$
$\Rightarrow\:b=5a=-15$
$\Rightarrow\:ab=45$
answered Jul 22, 2013 by rvidyagovindarajan_1
edited May 22, 2014 by rohanmaheshwari0831_1
 

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