Question

пожалуйста помогите с уравнениями ( решение через сумму коэффициентов квадратного уравнения)​

Answer 1

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Решаем по Виета

$x^2-14x+48=0\\x_{1}+x_{2}=-b\\x_{1}*x_{2}=d\\\\x_{1}+x_{2}=14\\x_{1}*x_{2}=48\\\\x_{1}=6\\x_{2}=8\\\\\\4)x^2-3x-10=0\\x_{1}+x_{2}=3\\x_{1}*x_{2}=-10\\\\x_{1}=-2\\x_{2}=5\\\\\\5)x^2+8x-20=0\\x_{1}+x_{2}=-8\\x_{1}*x_{2}=-20\\\\x_{1}=-10\\x_{2}=2\\\\\\6)x^2-9x+20=0\\x_{1}+x_{2}=9\\x_{1}*x_{2}=20\\\\x_{1}=5\\x_{2}=4\\\\\\7)x^2+17x-168=0\\x_{1}+x_{2}=-17\\x_{1}*x_{2}=-168\\\\x_{1}=-24\\x_{2}=7$

$8)x^2-21x+108=0\\x_{1}+x_{2}=21\\x_{1}*x_{2}=108\\\\x_{1}=9\\x_{2}=12\\\\\\9)x^2+x-2=0\\x_{1}+x_{2}=-1\\x_{1}*x_{2}=-2\\\\x_{1}=-2\\x_{2}=1\\\\\\10)x^2-x-2=0\\x_{1}+x_{2}=1\\x_{1}*x_{2}=-2\\\\x_{1}=-1\\x_{2}=2\\\\\\11)2x^2-5x+3=0\\D=25-6*4=25-24=1\\x_{1}=\frac{5+1}{4}=1,5\\x_{2}=\frac{5-1}{4}=1\\\\\\12)7x^2+8x+1=0 \\D=64-7*4=64-28=36=6^2\\x_{1}=\frac{-8+6}{14} =-\frac{1}{7} \\\\x_{2}=\frac{-8-6}{14}=-1$

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