Question

The sum of the roots of 2x2 + 8x - 3 = 0 Is

Answer 1

Find the roots of

2

x

2

+

8

x

−

3

=

0

by solving for

x

.

Exact Form:

x

=

−

4

±

√

22

2

Decimal Form:

x

=

0.34520787

…

,

−

4.34520787

…

Explanation:

I have used an Algebra calculator to check my answer given and my answer is correct.

Answer 2

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`2 {x}^(2) + 8x - 3 = 0`

`(x - ( ( - 8 + √(88) )/(4) ) \: )(x - ( ( - 8 - √(88) )/(4) ) \: ) = 0 \\`

Thus ;

`x - ( ( - 8 + √(88) )/(4) ) = 0 \\`

`x = ( - 8 + √(88) )/(4) \\`

This is one of the roots.

The other root is :

`x - ( ( - 8 - √(88) )/(4) ) = 0 \\`

`x = ( - 8 - √(88) )/(4) \\`

So sum of the roots is :

`( - 8 + √(88) )/(4) + ( - 8 - √(88) )/(4) = \\`

`( - 8 - 8 + √(88) - √(88) )/(4) = \\`

`( - 16)/(4) = - 4 \\`

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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 :

`sum \: \: of \: \: the \: roots = - (b)/(a) \\`

`b = coefficient \: \: of \: \: x`

`a = coefficient \: \: of \: \: {x}^(2)`

So ;

`sum \: \: of \: \: the \: \: roots \: = - (8)/(2) \\`

`sum \: \: of \: \: the \: \: roots = - 4`

Done...

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