Question

Find the sum and product of the roots. 3x 2 - 4x - 7 = 0

Answer 1

Answer:

Part 1) The sum of the roots is $4/3$

Part 2) The product of the roots is $-7/3$

Step-by-step explanation:

Step 1

Find the roots

we have

$3x^{2}-4x-7=0$

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

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

in this problem we have

$3x^{2}-4x-7=0$

so

$a=3\\b=-4\\c=-7$

substitute in the formula

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

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

$x=\frac{4(+/-)10} {6}$

$x1=\frac{4+10} {6}=7/3$

$x2=\frac{4-10} {6}=-1$  

Step 2

Find the sum of the roots

$x1+x2=(7/3)-1=4/3$

Step 3

Find the product of the roots

$x1*x2=(7/3)*(-1)=-7/3$

Answer 2

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

product = c/a  =  -7/3