Maharashtra BoardEnglish MediumSTD 10MathsQuadratic Equations2 Marks
Question
Solve the following quadratic equation:$3\sqrt7\text{x}^2+\text{4x}-\sqrt7=0$
✓
Answer
$3\sqrt7\text{x}^2+\text{4x}-\sqrt7=0$$\Rightarrow3\sqrt7\text{x}^2+7\text{x}-3\text{x}-\sqrt7=0$
$\Rightarrow\sqrt7\text{x}\big(3\text{x}+\sqrt7\big)-1\big(3\text{x}+\sqrt7\big)=0$
$\Rightarrow\big(\text{3x}+\sqrt{7}\big)\big(\sqrt7\text{x}-1\big)=0$
$\Rightarrow\text{3x}+\sqrt7=0$ or $\sqrt7\text{x}-1=0$
$\Rightarrow\text{3x}=-\sqrt7$ or $\text{x}=\frac{1}{\sqrt7}$
$\Rightarrow\text{x}=\frac{-\sqrt7}{3}$ or $\text{x}=\frac{1\times\sqrt7}{\sqrt7\times\sqrt7}=\frac{\sqrt7}{7}$
Hence, $\frac{-\sqrt7}{3}$ and $\frac{\sqrt7}{7}$ are the roots of the given equation.
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