Find the roots of the following quadratic equations by the factor… - Vidyadip

Question

Find the roots of the following quadratic equations by the factorisation method:
$3\sqrt{2}\text{x}^2-5\text{x}-\sqrt{2}=0.$

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Answer

Given equation is $3\sqrt{2}\text{x}^2-5\text{x}-\sqrt{2}=0$ $3\sqrt{2}\text{x}^2-(6\text{x}-\text{x})-\sqrt{2}=0$ [by splitting the middle term] $3\sqrt{2}\text{x}^2-(6\text{x}+\text{x})-\sqrt{2}=0$ $3\sqrt{2}\text{x}^2-3\sqrt{2}.\sqrt{2}\text{x}+\text{x}-\sqrt{2}=0$ $\Rightarrow\ 3\sqrt{2}\text{x}(\text{x}-\sqrt{2})+1(\text{x}-\sqrt{2})=0$ $\Rightarrow\ (\text{x}-\sqrt{2})(3\sqrt{2}\text{x}+1)=0$ Now, $\text{x}-\sqrt{2}=0\Rightarrow\ \text{x}=\sqrt{2}$ and $3\sqrt{2}\text{x}+1=0$ $\Rightarrow\ \text{x}=-\frac{1}{3\sqrt{2}}=\frac{-\sqrt{2}}{6}$Hence, the roots of the equation $3\sqrt{2}\text{x}^2-5\text{x}-\sqrt{2}=0$ are $-\frac{\sqrt{2}}{6}$ and $\sqrt{2}$.

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