Math, asked by swethavsky, 9 months ago

Find the roots of the quadratic equations by factorisation
1. x² – 3x – 10 = 0

Answers

Answered by Anonymous
12

Answer:

x = 5 or x = -2

Step-by-step explanation:

Given Quadratic equation ,

x² - 3x - 10 = 0

Splitting the middle term ,

we get

=> x² - 5x + 2x - 10 = 0

=> x( x - 5 ) + 2( x - 5 ) = 0

=> ( x - 5 )( x + 2 ) = 0

Therefore ,

x - 5 = 0 or x + 2 = 0

x = 5 or x = -2

Answered by Anonymous
9

AnswEr :

Given Equation : \normalsize\sf\ x^2 - 3x - 10

To find : \normalsize\sf\ Roots \: of \: Equation

\underline{\bigstar\:\textsf{By \: using \: Quadratic \: formula:}}

\normalsize\ : \implies\sf\ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

\normalsize\ : \implies\sf\ x = \frac{-(-3) \pm \sqrt{(3)^2 - 4 \times\ 1 \times\ (-10)}}{2 \times\ 1}

\normalsize\ : \implies\sf\ x = \frac{3 \pm \sqrt{9 - (-40)}}{2}

\normalsize\ : \implies\sf\ x = \frac{3 \pm \sqrt{9 + 40}}{2}

\normalsize\ : \implies\sf\ x = \frac{3 \pm \sqrt{49}}{2}

\normalsize\ : \implies\sf\ x = \frac{3 \pm 7}{2}

\normalsize\ : \implies\sf\ x = \frac{ 3 + 7}{2} \: \: or \: \:  \frac{3 - 7}{2}

\normalsize\ : \implies\sf\ x = \frac{\cancel{10}}{\cancel{2}} \: \: or \: \:  \frac{\cancel{-4}}{\cancel{2}}

\normalsize\ : \implies\sf\ x = 5 \: \: or \: \: -2

\normalsize\ : \implies{\underline{\boxed{\sf \red{ x = 5 \: \: or \: \: -2}}}}

\therefore\:\underline{\textsf{Hence, \: the \: value \: of \: x \: is}{\textbf{\: 5 \: or \: -2}}}

\underline{\bigstar\:\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\dashrightarrow\sf\ x = 5 \: or \: x = -2

\normalsize\dashrightarrow{\underline{\boxed{\sf \red{x = 5 \: or \:  -2}}}}

\therefore\:\underline{\textsf{Hence, \: the \: value \: of \: x \: is}{\textbf{\: 5 \: or \: -2}}}

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