Question

5) Solve x2 - 2x + 3 = 0 by using the quadratic formula​

Answer 1

Answer:

1+√2i and 1-√2i

Step-by-step explanation:

x2-2x+3 =0

On solving using quadratic formula, we get the roots of equation as 1+√2i and 1-√2i.

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Answer 2

$\begin{gathered}\frak{ \pink{Given : }}\sf{\;\;\; x^2 - 2x + 3 = \bf{0}}\end{gathered}$

$\begin{gathered}\frak{ \pink{To \: find : }}\sf{\;\;\; Value \: of \: x \: by \: using \: quadratic \: formula.}\end{gathered}$

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$\begin{gathered}\frak{ \pink{Solution : }}\end{gathered}$

Given that : x² - 2x + 3 = 0 and it is a quadratic equation in form of ax² + bx + c = 0.

Here,

• a = 1
• b = - 2
• c = 3

Quadratic formula :

• $\underline{\boxed{\bf x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a} }}$

Now, by substituting values :

$\sf : \implies x = \dfrac{-(-2)\pm \sqrt{(-2)^2 - 4(1)(3)}}{2(1)}$

$\sf : \implies x = \dfrac{2\pm \sqrt{4 - 4\times 1 \times 3}}{2\times 1}$

$\sf : \implies x = \dfrac{2\pm \sqrt{4 - 12}}{2}$

$\sf : \implies x = \dfrac{2\pm \sqrt{- 8}}{2}$

$\sf : \implies x = \dfrac{2\pm \sqrt{2 \times 2 \times - 2}}{2}$

$\sf : \implies x = \dfrac{2\pm 2 \sqrt{- 2}}{2}$

$\sf : \implies x = \dfrac{\cancel{2}(1\pm \sqrt{- 2})}{\cancel{2}}$

$\sf : \implies x = 1\pm\sqrt{- 2}$

$\: \:\:\: \: \: \: \: \: \: \: \: \: \: \: \: \pink{\underline{\boxed{\pmb{\frak{x = 1+\sqrt{- 2} \:or\: x = 1- \sqrt{- 2}}}}}}\:\bigstar$

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$\underline{ \bf Hence, \: value \: of \: x \: is \: \pink{1+\sqrt{- 2} \: or \: 1- \sqrt{- 2}}}.$