Question

find the roots of the following quadratic equations by factorisation
(1)
$x {}^{2} - 3x - 10 = 0$
​

Answer 1

Listen kid hate math and start loving GOD

Answer 2

$\huge\sf\pink{Answer}$

☞ Roots of the given Equation = 5 or -2

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$\huge\sf\blue{Given}$

➳ $\normalsize\sf\ x^2 - 3x - 10 = 0$

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$\huge\sf\gray{To \:Find}$

✭ $\normalsize\sf\ Roots \: of \: Equation$

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$\huge\sf\purple{Steps}$

$\underline{\bullet\textsf{\:By \: using \: Quadratic \: formula:}}$

$\normalsize\leadsto\sf\ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$\normalsize \leadsto\sf\ x = \dfrac{-(-3) \pm \sqrt{(3)^2 - 4 \times\ 1 \times\ (-10)}}{2 \times\ 1}$

$\normalsize \leadsto\sf\ x = \dfrac{3 \pm \sqrt{9 - (-40)}}{2}$

$\normalsize\leadsto\sf\ x = \dfrac{3 \pm \sqrt{9 + 40}}{2}$

$\normalsize\leadsto\sf\ x = \dfrac{3 \pm \sqrt{49}}{2}$

$\normalsize\leadsto\sf\ x = \dfrac{3 \pm 7}{2}$

$\normalsize\leadsto\sf\ x = \dfrac{ 3 + 7}{2} \: \: or \: \: \dfrac{3 - 7}{2}$

$\normalsize\leadsto\sf\ x = \dfrac{{10}}{{2}} \: \: or \: \: \dfrac{{-4}}{{2}}$

$\normalsize\orange{\leadsto\sf\ x = 5 \: \: or \: \: -2}$

$\underline{\bullet\:\textsf{By \: using \: Middle \: term \: factorization:}}$

$\normalsize\dashrightarrow\sf\ x^2 - 3x - 10 = 0$

$\normalsize\dashrightarrow\sf\ x^2 - 5x + 2x - 10 = 0$

$\normalsize\dashrightarrow\sf\ x(x - 5) + 2(x - 5) = 0$

$\normalsize\dashrightarrow\sf\ (x - 5)(x + 2) = 0$

$\normalsize\dashrightarrow\sf\ (x - 5) = 0 \: or \: (x + 2) = 0$

$\normalsize\dashrightarrow\sf\ x = 0 + 5 \: or \: x = 0 - 2$

$\normalsize\orange{\dashrightarrow\sf\ x = 5 \: or \: x = -2}$

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