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Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0
CBSE | Class 10 | Exercise 10C | Maths | Quadratic Equations | RS Aggarwal
Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0

The given equation is 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0

Comparing it with a x^{2}+b x+c=0, we get a=4 \sqrt{3}, b=5 and c=-2 \sqrt{3}

\therefore Discriminant, D=b^{2}-4 a c=5^{2}-4 \times 4 \sqrt{3} \times(-2 \sqrt{3})=25+96=121>0

So, the given equation has real roots.

Now, \sqrt{D}=\sqrt{121}=11

\begin{array}{l} \therefore \alpha=\frac{-b+\sqrt{D}}{2 a}=\frac{-5-11}{2 \times 4 \sqrt{3}}=\frac{6}{8 \sqrt{3}}=\frac{\sqrt{3}}{4} \\ \beta=\frac{-b-\sqrt{D}}{2 a}=\frac{-5-11}{2 \times 4 \sqrt{3}}=\frac{-16}{8 \sqrt{3}}=-\frac{2 \sqrt{3}}{3} \end{array}

Hence, \frac{\sqrt{3}}{4} and -\frac{2 \sqrt{3}}{3} are the root of the given equation.

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