Question

solve the quadratic equation using formuale
$\sf \implies x^2 - 10x + 21 = 0$​

Answer 1

x =( -b ± √(b2 - 4ac) ) / 2a

x = ( -(-10) ± √((-10)2 - 4121) ) / 2*1

= ( 10 ± √ 100 - 84 ) / 2 = ( 10 ± √ 16 ) 2 = (10 ± √ 16 ) / 2

= (10 ± 4 ) / 2

Solving this will give us the following two solutions:

x = (10 + 4) /2 = 14/2 = 7

x = (10 - 4) /2 = 6/2 = 3

Answer 2

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

• solve the equation using formulae $\sf x^2 - 10x + 21 = 0$

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

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

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

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☯ a = 1

☯ b = -10

☯ c = +21

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