Answer:
Explanation:
To find the value of c, we need to first find the roots of the equation. The product of the roots is given as 8, which means that the two roots must be -2 and -4. We can use this information to find the value of c by plugging the roots into the original equation and solving for c.
We start by setting the equation equal to 0, since this is what happens when a quadratic equation has roots. This gives us:
3x^2 + 30x + c = 0
Next, we use the fact that the roots are -2 and -4 to write the equation as a product of factors:
(x + 2)(x + 4) = 0
We can then expand the equation to get:
x^2 + 6x + 8 = 0
Finally, we can compare this equation with the original one to find the value of c. We see that the coefficients of the x^2 and x terms are the same in both equations, so the only difference is the constant term, which must be equal to 8. This means that the value of c is 8.
Therefore, the value of c in the equation y = 3x^2 + 30x + c is 8.