Question

Demonstrati identitatea: c la 2 - 7c+10=(c-2)(c-5)

Answer 1

$ax^{2} +bx+c=0$
Δ=b²-4ac
$x_{1} = \frac{-b- \sqrt{ b^{2} -4ac} }{2a} \\ x_{2} = \frac{-b+ \sqrt{ b^{2} -4ac} }{2a}$
$ax^{2} +bx+c=a(x- x_{1})(x- x_{2})$
$c^{2}-7c+10=0$
Δ=$(-7)^{2} -4*1*10=49-40=9 \\ c_{1} = \frac{-(-7)- \sqrt{9} }{2*1}= \frac{7-3}{2} = \frac{4}{2}=2 \\ c_{2} = \frac{-(-7)+ \sqrt{9} }{2*1} = \frac{7+3}{2} = \frac{10}{2} =5$
⇒$c^{2}-7c+10= (c-2)(c-5)$