Solve the following quadratic equation: `2x^2+sqrt(15)i x-i=0`

Answer

roots are `frac{1}{sqrt{2}},frac{1}{sqrt{2}}`.

Explanation

The quadratic equation is `2 x^{2}-2 sqrt{2} x+1=0.`

Comparing it with standard form of quadratic equation

` {ax}^{2}+{bx}+{c}=0`,

we get `a=2`, `b=-2 sqrt{2}`, `c=1 `

Therefore the roots of the quadratic equation are,

`{x}=frac{-{b} pm sqrt{{b}^{2}-4 {ac}}}{2 {a}}`

`=frac{-(-2 sqrt{2}) pm sqrt{(-2 sqrt{2})^{2}-4 times 2 times 1}}{2 times 2}`

` =frac{(2 sqrt{2}) pm sqrt{8-8}}{4}`

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