Question

Factorise x^2-3x+10=0

Answer 1

☯ Given

$\normalsize\sf\ x^2 - 3x - 10 x$

☯ To find

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answer 2

(x-5)(x+2)=0
roots: x=5 and x= -2
see attached photo for steps