Question

what is the exact roots x^2-2x+3​

Answer 1

$\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}$

$\sf\implies x^2 - 2x + 3 = 0$

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• compare the eq with $\sf{\underline{\bold{ax^2 + bx + c = 0 }}}$

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☯ a = 1

☯ b = -2

☯ c = 3

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now :-

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{x = \dfrac{ - b \pm \sqrt D }{2a }}}}}}}$

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$\sf{\underline{\boxed{\pink{\large{\mathfrak{ D = b^2 - 4ac }}}}}}$

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• finding value of D.

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$\sf\implies D = b^2 - 4ac$

$\sf\implies D = (-2)^2 - 4 \times 1 \times 3$

$\sf\implies D = 4 - 12$

$\sf\implies D = -8$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = -8 }}}}}}$

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• putting values in the eq.

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$\sf\implies x = \dfrac{ -b \pm\sqrt D }{2a}$

$\sf\implies x = \dfrac{ -( -2) \pm\sqrt {8} }{2\times 1 }$

$\sf\implies x = \dfrac{ 2 \pm 2\sqrt2 }{2}$

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✒$\sf x = \dfrac{ 2 + 2\sqrt 2 }{ 2 }$

$\implies x = {1+ \sqrt 2}$

$\sf{\underline{\boxed{\red{\large{\bold{ x = 1 + \sqrt 2 }}}}}}$

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✒$\sf x = \dfrac{ 2 - 2\sqrt 2 }{ 2 }$

$\implies x = {1 - \sqrt 2}$

$\sf{\underline{\boxed{\red{\large{\bold{ x = 1-\sqrt 2 }}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = 1 \pm \sqrt 2 }}}}}}$

Answer 2

Answer:

Hey

Step-by-step explanation:

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