Solve the following quadratic equation:x^2- (1+ 2 )x+ 2=0 - Vidyadip

Question

Solve the following quadratic equation:$\text{x}^2-\big(1+\sqrt2\big)\text{x}+\sqrt2=0$

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Answer

$\text{x}^2-\big(1+\sqrt2\big)\text{x}+\sqrt2=0$
$\Rightarrow\text{x}^2-1.\text{x}-\sqrt2\text{x}+\sqrt2=0$
$\Rightarrow\text{x}(\text{x}-1)-\sqrt2(\text{x}-1)=0$
$\Rightarrow(\text{x}-1)\big(\text{x}-\sqrt2\big)=0$
$\Rightarrow(\text{x}-1)=0$ or $\text{x}-\sqrt2=0$
$\Rightarrow\text{x}=1$ or $\text{x}=\sqrt2$
Hence, 1 and $\sqrt2$ are the roots of the given equation.

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