Question

Solve the following quadratic equation:

$i x^{2} - 4 x - 4 i = 0$

Accepted Answer

Given quadratic equation is $i x^{2} - 4 x - 4 i = 0$

$\Rightarrow i^{2} x^{2} - 4 i x - 4 i^{2} = 0$ [Multiplied both sides with $i$ ]

$\Rightarrow - x^{2} - 4 i x + 4 = 0$

$\Rightarrow x^{2} + 4 i x - 4 = 0$

On comparing the given equation to the general form of $a x^{2} + b x + c = 0$ , we get:

$a = 1, b = 4 i$ and $c = - 4$

Substituting these values as $a, b$ and $c$ in

$α = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a} or β = \frac{- b - \sqrt{b^{2} - 4 a c}}{2 a}$ [Assume that, $α, β$ are the roots of the given quadratic equation]

Therefore,

$α = \frac{- 4 i + \sqrt{{(4 i)}^{2} - 4 \times 1 \times (- 4)}}{2 a} or β = \frac{- 4 i - \sqrt{{(4 i)}^{2} - 4 \times 1 \times (- 4)}}{2 \times 1}$

$\Rightarrow α = \frac{- 4 i + \sqrt{16 i^{2} + 16}}{2} or β = \frac{- 4 i - \sqrt{16 i^{2} + 16}}{2}$

$\Rightarrow α = \frac{- 4 i + \sqrt{16 (- 1) + 16}}{2} or β = \frac{- 4 i - \sqrt{16 (- 1) + 16}}{2}$ $[∵ i^{2} = - 1]$

$\Rightarrow α = \frac{- 4 i}{2} or β = \frac{- 4 i}{2}$

$\Rightarrow α = - 2 i or β = - 2 i$

Hence, the roots of the given quadratic equation are: $- 2 i; - 2 i$ .

R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 14.2

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 14.2

Questions from R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 14.2 with Hints & Solutions

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