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[tex]2 {x}^{2} + 8x - 3 = 0[/tex]
[tex](x - ( \frac{ - 8 + \sqrt{88} }{4} ) \: )(x - ( \frac{ - 8 - \sqrt{88} }{4} ) \: ) = 0 \\ [/tex]
Thus ;
[tex]x - ( \frac{ - 8 + \sqrt{88} }{4} ) = 0 \\ [/tex]
[tex]x = \frac{ - 8 + \sqrt{88} }{4} \\ [/tex]
This is one of the roots.
The other root is :
[tex]x - ( \frac{ - 8 - \sqrt{88} }{4} ) = 0 \\ [/tex]
[tex]x = \frac{ - 8 - \sqrt{88} }{4} \\ [/tex]
So sum of the roots is :
[tex] \frac{ - 8 + \sqrt{88} }{4} + \frac{ - 8 - \sqrt{88} }{4} = \\ [/tex]
[tex] \frac{ - 8 - 8 + \sqrt{88} - \sqrt{88} }{4} = \\ [/tex]
[tex] \frac{ - 16}{4} = - 4 \\ [/tex]
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We have faster way to find ;
Remember from now on ,
If the quadratic functions have two roots ,
Sum of the roots is finding by following equation :
[tex]sum \: \: of \: \: the \: roots = - \frac{b}{a} \\ [/tex]
[tex]b = coefficient \: \: of \: \: x[/tex]
[tex]a = coefficient \: \: of \: \: {x}^{2} [/tex]
So ;
[tex]sum \: \: of \: \: the \: \: roots \: = - \frac{8}{2} \\ [/tex]
[tex]sum \: \: of \: \: the \: \: roots = - 4[/tex]
Done...
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