Login/Sign Up
Home » Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: .
Find the roots of the each of the following equations, if they exist, by applying the quadratic formula: 2 x^{2}+5 \sqrt{3} x+6=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: 2 x^{2}+5 \sqrt{3} x+6=0.

The given equation is 2 x^{2}+5 \sqrt{3} x+6=0.

Comparing it with a x^{2}+b x+c=0, we get
a=2, b=5 \sqrt{3} and c=6

\therefore Discriminant,
D=b^{2}-4 a c=(5 \sqrt{3})^{2}-4 \times 2 \times 6=75-48=27>0

So, the given equation has real roots.

Now, \sqrt{D}=\sqrt{27}=3 \sqrt{3}

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

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

i

More Material