Question

x² + 5x-6=0 quadratic formula
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Answer 1

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

• solve the equation using formulae $\sf x^2 + 5x -6 = 0$

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

$\sf\implies x^2 + 5x - 6 = 0$

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

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☯ a = 1

☯ b = 5

☯ c = -6

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

$\sf\implies D = (5)^2 - 4 \times 1 \times -6$

$\sf\implies D = 25 + 24$

$\sf\implies D = 49$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 49}}}}}}$

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• putting values in the eq.

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

$\sf\implies x = \dfrac{ -(5) \pm\sqrt {49} }{2\times 1 }$

$\sf\implies x = \dfrac{ -5 \pm 7 }{2}$

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✒$\sf x = \dfrac{ -5 + 7 }{ 2 }$

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

$\implies x = 1$

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

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✒$\sf x = \dfrac{ -5 -7 }{ 2 }$

$\implies x = \dfrac {-12}{2}$

$\implies x = -6$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = -6 }}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x =1 \: or \:-6 }}}}}}$