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Formula
Relationship between roots and coefficients
Answer
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$$4 x ^ { 2 } - 9 = 0$$
$\alpha + \beta = 0 , \alpha \beta = - \dfrac { 9 } { 4 }$
Find the sum and product of the two roots of the quadratic equation
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 9 } = \color{#FF6800}{ 0 }$
$ $ In the quadratic equation $ ax^{2}+bx+c=0 $ , if the two roots are $ \alpha, \beta $ , then it is $ \alpha + \beta =-\dfrac{b}{a} $ , $ \alpha\times\beta=\dfrac{c}{a}$
$\color{#FF6800}{ \alpha } \color{#FF6800}{ + } \color{#FF6800}{ \beta } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 0 } { 4 } } , \color{#FF6800}{ \alpha } \color{#FF6800}{ \beta } = \color{#FF6800}{ \dfrac { - 9 } { 4 } }$
$\alpha + \beta = - \color{#FF6800}{ \dfrac { 0 } { 4 } } , \alpha \beta = \dfrac { - 9 } { 4 }$
$ $ If the numerator is 0, it is equal to 0 $ $
$\alpha + \beta = - \color{#FF6800}{ 0 } , \alpha \beta = \dfrac { - 9 } { 4 }$
$\alpha + \beta = \color{#FF6800}{ - } \color{#FF6800}{ 0 } , \alpha \beta = \dfrac { - 9 } { 4 }$
$ $ 0 has no sign $ $
$\alpha + \beta = \color{#FF6800}{ 0 } , \alpha \beta = \dfrac { - 9 } { 4 }$
$\alpha + \beta = 0 , \alpha \beta = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 9 } } { 4 }$
$ $ Move the minus sign to the front of the fraction $ $
$\alpha + \beta = 0 , \alpha \beta = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 } { 4 } }$
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