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General Equation of Circle S=0

If the curve ...

Question

If the curve $y = c_{1} e^{m_{1} x} + c_{2} e^{m_{3} x}$ , where $c_{1}, c_{2}, c_{3}$ are arbitrary constants and $m_{1}, m_{2}, m_{3}$ are roots of $m^{3} - 7 m + 6 = 0$ , then the sum of product of two roots at a time is,

0

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Solution

The correct option is A $- 7$
$m^{3} - 7 m + 6$

$m_{1}, m_{2}, m_{3}$ are roots

sum of product of two roots at a time $= m_{1} m_{2} + m_{1} m_{3} + m_{2} m_{3}$

$m_{1} m_{2} + m_{2} m_{3} + m_{1} m_{3} = \frac{- 7}{1}$

$= - 7$ .

Hence option $C$ is the answer.

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Similar questions

y = c_{1} e^{m_{1} x} + c_{2} e^{m_{3} x}

c_{1}, c_{2}, c_{3}

m_{1}, m_{2}, m_{3}

m^{3} - 7 m + 6 = 0

y = m_{1} x + c_{1}, y = m_{2} x + c_{2}

y = m_{3} + c_{3}

m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0

y = C_{1} + C_{2} e^{x} + C_{3} e^{- 2 x + C_{4}}

C_{1}, C_{2}, C_{3}, C_{4}

y = c_{1} e^{c_{2} x},

c_{1}

c_{2}

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T_{1}, T_{2}, T_{3}

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