Question

Solve the following quadratic equation

$\sqrt{3} x^{2} - \sqrt{2} x + 3 \sqrt{3} = 0$ .

Accepted Answer

Given quadratic equation is $\sqrt{3} x^{2} - \sqrt{2} x + 3 \sqrt{3} = 0$

Comparing the given quadratic equation to the general from $a x^{2} + b x + c = 0$ we get
$a = \sqrt{3}, b = - \sqrt{2}, c = 3 \sqrt{3}$

Substitute these values in below formula
$α = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 a}$ 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, $α = \frac{\sqrt{2} + \sqrt{2 - 4 \times \sqrt{3} \times 3 \sqrt{3}}}{2 \times \sqrt{3}}$ or $β = \frac{\sqrt{2} - \sqrt{2 - 4 \times \sqrt{3} \times 3 \sqrt{3}}}{2 \times \sqrt{3}}$

$\Rightarrow α = \frac{\sqrt{2} + \sqrt{2 - 36}}{2 \sqrt{3}}$ or $β = \frac{\sqrt{2} - \sqrt{2 - 36}}{2 \sqrt{3}}$

$\Rightarrow α = \frac{\sqrt{2} + \sqrt{- 34}}{2 \sqrt{3}}$ or $β = \frac{\sqrt{2} + \sqrt{- 34}}{2 \sqrt{3}}$ $[∵ i = \sqrt{- 1}, \sqrt{- 34} = \sqrt{34} i]$

$\Rightarrow α = \frac{\sqrt{2} + i \sqrt{34}}{2 \sqrt{3}}$ or $β = \frac{\sqrt{2} - i \sqrt{34}}{2 \sqrt{3}}$
Hence, the roots of the given quadratic equation are: $\frac{\sqrt{2} \pm i \sqrt{34}}{2 \sqrt{3}}$ .

R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE 14.1

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE 14.1

Questions from R D Sharma Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE 14.1 with Hints & Solutions

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