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Formula
Number of solution
Answer
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$$x ^ { 2 } + 5 x + 3 = 0$$
$ $ 2 real roots $ $
Find the number of solutions
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0 }$
$ $ Determine the number of roots using discriminant, $ D=b^{2}-4ac $ from quadratic equation, $ ax^{2}+bx+c=0$
$\color{#FF6800}{ D } = \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$D = \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 3$
$ $ Calculate power $ $
$D = \color{#FF6800}{ 25 } - 4 \times 1 \times 3$
$D = 25 - 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \times 3$
$ $ Multiplying any number by 1 does not change the value $ $
$D = 25 - 4 \times 3$
$D = 25 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 }$
$ $ Multiply $ - 4 $ and $ 3$
$D = 25 \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$D = \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 12 }$
$ $ Subtract $ 12 $ from $ 25$
$D = \color{#FF6800}{ 13 }$
$\color{#FF6800}{ D } = \color{#FF6800}{ 13 }$
$ $ Since $ D>0 $ , the number of real root of the following quadratic equation is 2 $ $
$ $ 2 real roots $ $
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