Question

factorise x^2 + 6x - 10 = 0 using formula​

Answer 1

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

$\sf\implies x^2 + 6x - 10 = 0$

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

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☯ a = 1

☯ b = 6

☯ c = -10

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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.⠀⠀⠀⠀⠀⠀⠀

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

$\sf\implies D = (6)^2 - 4 \times 1 \times -10$

$\sf\implies D = 36 + 40$

$\sf\implies D = 76$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 76}}}}}}$

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• putting values in the eq.

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

$\sf\implies x = \dfrac{ -( 6) \pm\sqrt {76} }{2\times 1 }$

$\sf\implies x = \dfrac{ -6 \pm 2\sqrt{19} }{2}$

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✒$\sf x = \dfrac{ -6 - 2\sqrt{19}}{ 2 }$

$\implies x = {-3 -\sqrt{19}}$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = -3 - \sqrt{19} }}}}}}$

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✒$\sf x = \dfrac{ -6 + 2\sqrt{19} }{ 2 }$

$\implies x = -3 +2\sqrt{19}$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = -3 + \sqrt{19}}}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = -3 -\sqrt{19} \: or \:-3 + \sqrt{19}}}}}}}$