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

Question

Dr. Abubacker · Accepted Answer

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

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

Explanation

Reviewed by Dr. Abubacker

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