Question

factorise x^2 - 10x + 21 = 0 using quadratic formula​

Answer 1

Step-by-step explanation:

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Answer 2

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

$\sf\implies x^2 - 10x + 21 = 0$

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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 = -27

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

$\sf\implies D = (-10)^2 - 4 \times 1 \times 21$

$\sf\implies D = 100 - 84$

$\sf\implies D = 16$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 16}}}}}}$

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putting values in the eq.

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

$\sf\implies x = \dfrac{ -( -10) \pm\sqrt {16} }{2\times 1 }$

$\sf\implies x = \dfrac{ 10 \pm 4 }{2}$

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✒$\sf x = \dfrac{ 10 + 4 }{ 2 }$

$\implies x = \dfrac {14}{2}$

$\implies x = 7$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = 7 }}}}}}$

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✒$\sf x = \dfrac{ 10 - 4 }{ 2 }$

$\implies x = \dfrac {6}{2}$

$\implies x = 3$

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

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = 7 \: or \: 3 }}}}}}$