Question

Дано квадратное уравнение x2−14,2x−1,4=0, укажи сумму и произведение корней.
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Answer 1

Ответ: 4 и -45,01

Объяснение:

$x^{2} -14,2x-1,4=0\\D=b^{2} -4ac = 14,2^{2} -4*1*1,4=196.04\\x_{1} =\frac{-b+\sqrt{D} }{2a} =\frac{4+\sqrt{196,04}}{2} =\frac{4+2\sqrt{49.01}}{2} =\frac{2*(2+\sqrt{49.01}}{2} =2+\sqrt{49.01} \\x_{2} =\frac{-b-\sqrt{D} }{2a} =\frac{4-\sqrt{196,04}}{2} =\frac{4-2\sqrt{49.01}}{2} =\frac{2*(2-\sqrt{49.01}}{2} =2-\sqrt{49.01} \\x_{1} +x_{2} = 2+\sqrt{49.01} +2-\sqrt{49.01} =4\\x_{1} *x_{2} =(2+\sqrt{49.01})*(2-\sqrt{49.01}) = 2^{2} -(\sqrt{49.01}) ^{2} =4-49.01=-45.01$