Question

Find the roots of the quadratic equations by using the quadratic formula method: -x^2 + 7x-10 = 0

Answer 1

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

• solve the equation using formulae $\sf x^2 + 7x - 10 = 0$

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

$\sf\implies x^2 + 7x - 10= 0$

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

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☯ a = 1

☯ b = 7

☯ 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.

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

$\sf\implies D = (7)^2 - 4 \times 1 \times -10$

$\sf\implies D = 49 + 40$

$\sf\implies D = 89$

$\sf{\underline{\boxed{\blue{\large{\bold{ D = 89}}}}}}$

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• putting values in the eq.

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

$\sf\implies x = \dfrac{ -( 7 ) \pm\sqrt {89} }{2\times 1 }$

$\sf\implies x = \dfrac{ 7 \pm \sqrt{89} }{2}$

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✒$\sf x = \dfrac{ 7 + \sqrt{89}}{ 2 }$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = \dfrac{ 7 + \sqrt{89}}{2} }}}}}}$

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⠀✒$\sf x = \dfrac{ 7 - \sqrt{89}}{ 2 }$

$\sf{\underline{\boxed{\purple{\large{\bold{ x = \dfrac{ 7 - \sqrt{89}}{2} }}}}}}$

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$\sf{\underline{\boxed{\purple{\large{\bold{ x = \dfrac{7 - \sqrt{89}}{2} \: or \: \dfrac{ 7 +\sqrt{89}}{2}}}}}}}$