Question

3xelevado a 2+5=x (x-3)+10

Answer 1

$3 x^{2} +5=x(x-3)+10\\\\\\ 3 x^{2} +5= x^{2} -3x+10\to \\\\ 3 x^{2} +5- x^{2} +3x-10=0\to \\\\ 2 x^{2} +3x-5=0\\\\ a=2;b=3;c=-5\\\\\\ \Delta=b^2-4ac\to \Delta=3^2-4*2*(-5)\to \Delta=9+40\to \Delta=49\\\\\\ x' \neq x''\\\\\\ x= \frac{-b \pm \sqrt{ \Delta} }{2a} \to x= \frac{-3 \pm \sqrt{49} }{2*2} \to x= \frac{-3 \pm 7 }{4} \to \\\\\\ x'= \frac{-3+ 7 }{4} \to x'= \frac{4 }{4} \to x'=1\\\\\\ x''= \frac{-3 -7 }{4} \to x''= \frac{-10}{4} \to x''= \frac{-5}{2} \\\\\\ S=( \frac{-5}{2} ;1)$


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