Respuesta :

sum of the roots  = -b/a  = -(-4)/ 3  = 4/3

product = c/a  =  -7/3

Answer:

Part 1) The sum of the roots is [tex]4/3[/tex]

Part 2) The product of the roots is [tex]-7/3[/tex]

Step-by-step explanation:

Step 1

Find the roots

we have

[tex]3x^{2}-4x-7=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}-4x-7=0[/tex]

so

[tex]a=3\\b=-4\\c=-7[/tex]

substitute in the formula

[tex]x=\frac{-(-4)(+/-)\sqrt{-4^{2}-4(3)(-7)}} {2(3)}[/tex]

[tex]x=\frac{4(+/-)\sqrt{16^{2}+84}} {6}[/tex]

[tex]x=\frac{4(+/-)10} {6}[/tex]

[tex]x1=\frac{4+10} {6}=7/3[/tex]

[tex]x2=\frac{4-10} {6}=-1[/tex]  

Step 2

Find the sum of the roots

[tex]x1+x2=(7/3)-1=4/3[/tex]

Step 3

Find the product of the roots

[tex]x1*x2=(7/3)*(-1)=-7/3[/tex]

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